# Topic Questions: • understand the relationship between a graph and its associated algebraic equation, and use the relationship between points of intersection of graphs and solutions of equations — 9709 P1 Coordinate geometry > 39 9709 P1 Coordinate geometry topic questions (135 marks) on understand the relationship between a graph and… — 24 papers, 2020–2026. Open the exact… - Canonical HTML: https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/coordinate-geometry/understand-the-relationship-between-a-graph-and-its-associated-algebraic-equation-and/ - Markdown mirror: https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/coordinate-geometry/understand-the-relationship-between-a-graph-and-its-associated-algebraic-equation-and/index.md --- CIE IAL · Mathematics · 9709 P1 · Coordinate geometry 39 9709 P1 Coordinate geometry topic questions are tagged to this syllabus point across 24 papers (2020–2026). Only the parts whose knowledge graph matches this syllabus statement are counted, and the table shows which parts of each question are involved. - 39 topic questions - 24 papers - 135 tagged marks - 21.0% of topic questions - 20.0% of topic marks - 2020–2026 - Syllabus 2020–2027 - [All 9709 P1 Coordinate geometry topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/coordinate-geometry/) - [All paper codes](https://www.examsci.com/topics/) Core finding **This Coordinate geometry syllabus point appears in 24 9709 P1 papers across 2020–2026, contributing 39 topic questions and 135 marks.** The most recent appearance is 9709/12 May/June 2026. That equals 21.0% of the 186 topic questions and 20.0% of the 676 marks tagged to Coordinate geometry. Only parts tagged to this subtopic are counted, so a four-part question can contribute one item and one part's marks. The table lists every matching question, its tagged parts and marks, with a link back to the paper page. Sessions are newest first, so the statement can be traced back through the full paper history. ## Topic questions by session Newest sessions first. Parts and marks count only the parts tagged to this subtopic; “x of y parts” shows how much of the question is tagged elsewhere. Select the paper cell to open the matching question on the paper page, or use **Go to Practice Hub** to answer that exact question in the Interactive Practice Hub. | Paper | Question | Type | Parts | Marks | Difficulty | Practice | | --- | --- | --- | --- | --- | --- | --- | | [**9709/12** May/June 2026 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2026-may-june-9709-12/#q-8) | **Q8** Circle Equation and Chord Length - CIE A-Level Maths 2026 Jun Paper 12 Q8 | FRQ | 1 of 2 parts ((b)) | 7 of 11 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=11194fbb-d7f0-45e6-87b6-973cdafbc920&question_id=24fe9184-d187-4ebf-8ac2-4ba8038468d5&source_detail=9709%2F12+May%2FJune+2026) | | [**9709/15** May/June 2026 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2026-may-june-9709-15/#q-6) | **Q6** Line and Curve Intersection Discriminant - CIE Pure Mathematics 2026 Jun Paper 15 Q6 | FRQ | 1 part | 4 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=05b20104-0aad-4794-b387-5aaa042ea528&question_id=e94961e0-5fab-4d42-8516-14f06a3ef4ae&source_detail=9709%2F15+May%2FJune+2026) | | [**9709/15** May/June 2026 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2026-may-june-9709-15/#q-10) | **Q10** Area of Shaded Region Between Line and Curve - CIE Pure Mathematics 2026 Jun Paper 15 Q10 | FRQ | 1 part | 7 | Hard | [Go to Practice Hub](https://www.examsci.com/practice?set_id=05b20104-0aad-4794-b387-5aaa042ea528&question_id=4cd332ef-baba-4d18-b2e4-3ec5d939eca8&source_detail=9709%2F15+May%2FJune+2026) | | [**9709/12** October/November 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2025-october-november-9709-12/#q-6) | **Q6** Trigonometric Graph and Equations - CIE A-Level Maths 2025 Nov Paper 12 Q6 | FRQ | 2 of 4 parts ((b)(i), (b)(ii)) | 2 of 9 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=c80cfa73-10a0-4c4a-a902-9f861759760f&question_id=e33916e0-860c-4edb-9f40-f6aea61eaa06&source_detail=9709%2F12+October%2FNovember+2025) | | [**9709/11** May/June 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2025-may-june-9709-11/#q-6) | **Q6** Intersection of Curve and Line - CIE Pure Mathematics 2025 Jun Paper 11 Q6 | FRQ | 1 of 2 parts ((b)) | 5 of 9 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=7ab62c6c-c216-4c43-b712-b50225a649b8&question_id=c1078414-e6a2-4811-a845-4768125c5bc2&source_detail=9709%2F11+May%2FJune+2025) | | [**9709/12** May/June 2025 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2025-may-june-9709-12/#q-5) | **Q5** Trigonometric Graph and Intersection - CIE 9709 Pure Mathematics 1 2025 Jun Paper 12 Q5 | FRQ | 1 of 3 parts ((c)) | 1 of 5 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=67393ac1-93c5-4264-b8b5-4a571c09a650&question_id=ab6493ee-419f-442e-8453-8ed60bd8bccf&source_detail=9709%2F12+May%2FJune+2025) | | [**9709/12** October/November 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2024-october-november-9709-12/#q-1) | **Q1** Trigonometric Graph Parameters - CIE A-Level Maths 2024 Nov Paper 12 Q1 | FRQ | 2 of 3 parts ((b)(i), (b)(ii)) | 2 of 5 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=724ea49a-6892-4803-a02f-4c173d9c5a72&question_id=254ec4d2-1b5e-4dd2-8bb7-96c319bb309f&source_detail=9709%2F12+October%2FNovember+2024) | | [**9709/12** October/November 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2024-october-november-9709-12/#q-9) | **Q9** Intersection of Quadratic Curve and Line - CIE A-Level Maths 2024 Nov Paper 12 Q9 | FRQ | 1 of 2 parts ((a)) | 7 of 10 on the paper | Hard | [Go to Practice Hub](https://www.examsci.com/practice?set_id=724ea49a-6892-4803-a02f-4c173d9c5a72&question_id=2e28b198-1272-47db-8cb8-6f44afdc933a&source_detail=9709%2F12+October%2FNovember+2024) | | [**9709/13** October/November 2024 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2024-october-november-9709-13/#q-9) | **Q9** Area Between Two Cubic Curves - CIE Pure Mathematics 2024 Nov Paper 13 Q9 | FRQ | 1 of 2 parts ((a)) | 3 of 7 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d6efe97b-7a31-419e-959f-4bf66d69ec85&question_id=9749eb12-3990-4057-8012-62191e51cc0e&source_detail=9709%2F13+October%2FNovember+2024) | | [**9709/11** October/November 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2023-october-november-9709-11/#q-2) | **Q2** Line and Curve Intersection - CIE Mathematics 2023 Nov Paper 11 Q2 | FRQ | 1 part | 4 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=a8d9ce7e-4b0c-40c4-b2e8-bbee159040f1&question_id=e6f876c0-8dfa-4fc3-9da5-34cc01aeeaff&source_detail=9709%2F11+October%2FNovember+2023) | | [**9709/11** October/November 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2023-october-november-9709-11/#q-8) | **Q8** Area Between Curves with Substitution - CIE Mathematics 2023 Nov Paper 11 Q8 | FRQ | 1 of 2 parts ((a)) | 4 of 9 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=a8d9ce7e-4b0c-40c4-b2e8-bbee159040f1&question_id=7ff13394-2fb3-4797-a649-32c4eb03ea03&source_detail=9709%2F11+October%2FNovember+2023) | | [**9709/12** October/November 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2023-october-november-9709-12/#q-9) | **Q9** Area Between Intersecting Curves - CIE 9709 P12 2023 Nov Q9 | FRQ | 1 of 2 parts ((a)) | 4 of 9 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=1b2438c6-7fe6-48d0-b79c-a23660af16f3&question_id=6bf10921-f35a-46b4-92bd-b696979bd09e&source_detail=9709%2F12+October%2FNovember+2023) | | [**9709/11** May/June 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2023-may-june-9709-11/#q-7) | **Q7** Sine Curve Transformation and Intersection - CIE 9709 Pure Mathematics June 2023 Paper 11 Q7 | FRQ | 1 of 3 parts ((c)) | 1 of 5 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=0dc71803-e90c-4c78-aca9-ca1013b0ad45&question_id=bfc08744-a364-46d5-b132-a2a9a5a82bd1&source_detail=9709%2F11+May%2FJune+2023) | | [**9709/13** May/June 2023 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2023-may-june-9709-13/#q-9) | **Q9** Curve Integration and Tangent Intersection - CIE Pure Mathematics 1 2023 Jun Q9 | FRQ | 2 of 3 parts ((b), (c)) | 6 of 10 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=508e4929-f4d6-4905-b3b8-773abcf19d42&question_id=a6636899-0a64-493a-bd69-bd955eec259a&source_detail=9709%2F13+May%2FJune+2023) | | [**9709/11** May/June 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2022-may-june-9709-11/#q-7) | **Q7** Intersection and Area Between Curve and Line - CIE 9709 s22 qp 11 Q7 | FRQ | 1 of 2 parts ((a)) | 4 of 9 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=13d1cb95-4ad2-4921-a6af-70e64afc07b9&question_id=a9072e6b-e1a3-4cff-8233-35f9319e90bf&source_detail=9709%2F11+May%2FJune+2022) | | [**9709/12** May/June 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2022-may-june-9709-12/#q-5) | **Q5** Intersection and Tangency of Line and Curve - CIE P1 2022 Jun Q5 | FRQ | 2 parts ((a), (b)) | 9 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=0db3f5fb-5aad-45cf-9535-2533b5052d2e&question_id=6ee6cf0f-06cf-4091-9017-5e653f51774e&source_detail=9709%2F12+May%2FJune+2022) | | [**9709/13** May/June 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2022-may-june-9709-13/#q-11) | **Q11** Tangent and Normal Parametric Intersections - CIE Pure Mathematics 2022 Jun Paper 13 Q11 | FRQ | 1 of 2 parts ((a)) | 6 of 10 on the paper | Hard | [Go to Practice Hub](https://www.examsci.com/practice?set_id=90bad8f3-9168-4467-ba03-80154a74af3f&question_id=e4ba4e76-a9bf-4d2f-889d-37c74cc2479f&source_detail=9709%2F13+May%2FJune+2022) | | [**9709/12** March 2022 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2022-march-9709-12/#q-2) | **Q2** Intersection of Curve and Line - CIE 9709 Pure Mathematics 1 March 2022 Paper 12 Q2 | FRQ | 1 part | 5 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=69bdfe18-33b4-4159-a3eb-d1337cf54642&question_id=1a0047fd-4e2b-458d-aeea-ad02e7cf0e2a&source_detail=9709%2F12+March+2022) | | [**9709/11** October/November 2021 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2021-october-november-9709-11/#q-2) | **Q2** Non-intersecting Line and Quadratic Curve - CIE 9709 Pure Mathematics 2021 Nov Paper 11 Q2 | FRQ | 1 part | 5 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=a3a8f7c1-53b0-41e7-a3ba-261116294db7&question_id=affa7195-4ec1-4bc1-8372-0c7b4437232e&source_detail=9709%2F11+October%2FNovember+2021) | | [**9709/11** October/November 2021 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2021-october-november-9709-11/#q-5) | **Q5** Trigonometric Function Graph and Line Intersections - CIE 9709 Pure Mathematics 2021 Nov Paper 11 Q5 | FRQ | 2 of 3 parts ((b)(i), (b)(ii)) | 2 of 5 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=a3a8f7c1-53b0-41e7-a3ba-261116294db7&question_id=d3c8a01f-73a8-40cd-94e2-23175bd0ccb7&source_detail=9709%2F11+October%2FNovember+2021) | | [**9709/11** May/June 2021 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2021-may-june-9709-11/#q-6) | **Q6** Tangent to Quadratic Curve - CIE 9709 P1 2021 Jun Q6 | FRQ | 1 part | 5 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=c82991d4-eca8-4d00-8838-22d687973d23&question_id=a67d51be-c007-4f46-982b-3d9d86b59131&source_detail=9709%2F11+May%2FJune+2021) | | [**9709/12** May/June 2021 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2021-may-june-9709-12/#q-3) | **Q3** Limit of Chord Gradients - CIE A-Level Maths 2021 Jun P12 Q3 | FRQ | 1 of 3 parts ((a)) | 1 of 4 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=d18b9b1e-0c99-4c74-9a96-27220d8ddf82&question_id=d7e92d17-aadf-45d5-ba44-1f72bbb7bb70&source_detail=9709%2F12+May%2FJune+2021) | | [**9709/13** May/June 2021 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2021-may-june-9709-13/#q-3) | **Q3** Tangent Line to Quadratic Curve - CIE P1 2021 Jun Q3 | FRQ | 1 part | 6 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=9533759f-bf57-4dc6-8e41-819edf45735e&question_id=29a048d5-1a17-4b5a-b278-4a9ac03eef89&source_detail=9709%2F13+May%2FJune+2021) | | [**9709/12** March 2021 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2021-march-9709-12/#q-4) | **Q4** Line and Curve Intersection Discriminant - CIE Pure Mathematics 2021 Mar Paper 12 Q4 | FRQ | 1 part | 5 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=c5921612-6447-44d9-ac13-97397140f1f1&question_id=adac604f-c801-4a0d-a984-d89ea432afa2&source_detail=9709%2F12+March+2021) | | [**9709/12** March 2021 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2021-march-9709-12/#q-11) | **Q11** Curve Analysis Integration and Stationary Points - CIE Pure Mathematics 2021 Mar Paper 12 Q11 | FRQ | 1 of 4 parts ((a)) | 2 of 12 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=c5921612-6447-44d9-ac13-97397140f1f1&question_id=dea5add4-a8c6-4881-89c8-bd7244f9f010&source_detail=9709%2F12+March+2021) | | [**9709/12** October/November 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2020-october-november-9709-12/#q-3) | **Q3** Intersection of Line and Quadratic Curve - CIE 9709 Nov 2020 Paper 12 Q3 | FRQ | 1 part | 5 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=f4ff68c4-3b93-4e28-8283-1fff16750c61&question_id=291e1a9d-17b9-4fbc-9166-e97a87687c56&source_detail=9709%2F12+October%2FNovember+2020) | | [**9709/12** October/November 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2020-october-november-9709-12/#q-11) | **Q11** Trigonometric Function Transformations and Intersection - CIE 9709 Nov 2020 Paper 12 Q11 | FRQ | 3 of 7 parts ((c)(i), (c)(ii), (c)(iii)) | 3 of 11 on the paper | Easy | [Go to Practice Hub](https://www.examsci.com/practice?set_id=f4ff68c4-3b93-4e28-8283-1fff16750c61&question_id=15bd3f04-e799-4860-a17c-0e8f09bf3a42&source_detail=9709%2F12+October%2FNovember+2020) | | [**9709/13** October/November 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2020-october-november-9709-13/#q-4) | **Q4** Intersection of Line and Curve using Discriminant - CIE 9709 Nov 2020 P13 Q4 | FRQ | 1 part | 5 | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=95fd6ce4-f7e7-4fab-88ee-1c4b6760c30b&question_id=16ec5444-edb4-4652-81c3-4ccdba5a0d31&source_detail=9709%2F13+October%2FNovember+2020) | | [**9709/13** October/November 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2020-october-november-9709-13/#q-11) | **Q11** Circle Geometry and Tangent Properties - CIE 9709 Nov 2020 P13 Q11 | FRQ | 1 of 4 parts ((d)) | 3 of 12 on the paper | Hard | [Go to Practice Hub](https://www.examsci.com/practice?set_id=95fd6ce4-f7e7-4fab-88ee-1c4b6760c30b&question_id=7b0aaffe-c03b-4ed3-a746-79c890ccff52&source_detail=9709%2F13+October%2FNovember+2020) | | [**9709/11** May/June 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2020-may-june-9709-11/#q-5) | **Q5** Intersection of Line and Hyperbola - CIE Pure Mathematics 2020 Jun Paper 11 Q5 | FRQ | 1 of 2 parts ((a)) | 3 of 6 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2a32622e-5734-4055-b968-5b1e651337c0&question_id=069afb0b-4a5f-49f9-abda-81cad25e0df4&source_detail=9709%2F11+May%2FJune+2020) | | [**9709/11** May/June 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2020-may-june-9709-11/#q-11) | **Q11** Volume of Revolution Bounded Region - CIE Pure Mathematics 2020 Jun Paper 11 Q11 | FRQ | 1 of 2 parts ((a)) | 6 of 12 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=2a32622e-5734-4055-b968-5b1e651337c0&question_id=cd38341e-823f-44bf-85e5-dd5ad50d6cac&source_detail=9709%2F11+May%2FJune+2020) | | [**9709/12** May/June 2020 · CIE IAL](https://www.examsci.com/past-papers/cie-ial/mathematics/9709-p1/2020-may-june-9709-12/#q-11) | **Q11** Circle Equation and Tangents - CIE P1 2020 Jun Q11 | FRQ | 1 of 4 parts ((d)) | 3 of 11 on the paper | Medium | [Go to Practice Hub](https://www.examsci.com/practice?set_id=9275aff7-1c76-429c-8092-211f890344a0&question_id=d67b9909-4099-4f5a-91dc-6fc2eb94276b&source_detail=9709%2F12+May%2FJune+2020) | ## Related topic questions in Coordinate geometry - [• find the equation of a straight line given sufficient information](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/coordinate-geometry/find-the-equation-of-a-straight-line-given-sufficient-information/) — 51 question items · 35 papers — 209 marks · 2020–2026 - [• interpret and use any of the forms $y=mx+c$, $y-y_1=m(x-x_1)$, $ax+by+c=0$ in solving problems](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/coordinate-geometry/interpret-and-use-any-of-the-forms-y-mx-c-y-y-1-m-x-x-1-ax-by-c-0-in-solving-problems/) — 19 question items · 15 papers — 78 marks · 2020–2026 - [• understand that the equation $(x-a)^2+(y-b)^2=r^2$ represents the circle with centre $(a,b)$ and radius $r$](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/coordinate-geometry/understand-that-the-equation-x-a-2-y-b-2-r-2-represents-the-circle-with-centre-a-b/) — 56 question items · 41 papers — 208 marks · 2020–2026 - [• use algebraic methods to solve problems involving lines and circles](https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/coordinate-geometry/use-algebraic-methods-to-solve-problems-involving-lines-and-circles/) — 95 question items · 44 papers — 386 marks · 2020–2026 ## Topic question rules and edge cases **How many topic questions cover this syllabus point?** 32 question stems cover this subtopic across 24 papers, but only 39 tagged parts and 135 marks belong to it. Other parts of the same questions are assessed under different statements and are excluded from this page. **Which papers include this subtopic?** The table lists every matching session from 2020–2026. Each row links to the question anchor on the paper page, where the full paper context and practice entry point are available. **Why can one question appear under several subtopics?** The parts of one question can assess different syllabus statements. Each part is counted under its own subtopics, so the same question stem can appear on several subtopic pages while each page lists only the parts and marks tagged to that statement. **Can I practise these questions with AI marking?** Yes. Open a paper from the table and use the Interactive Practice Hub entry point. The page itself is static HTML so search engines and retrieval agents can read the full question list without executing JavaScript. --- Full page with native tables, bar charts and Practice Hub links: https://www.examsci.com/topics/cie-ial/mathematics/9709-p1/coordinate-geometry/understand-the-relationship-between-a-graph-and-its-associated-algebraic-equation-and/