--- title: "Reading solutions from a graph" description: "Use graphs of linear and quadratic functions to estimate output values for given inputs, find approximate solutions to equations, and interpret graphical information in real-world contexts" canonical: https://lightmysky.com/learn/mathematics/reading-solutions-from-a-graph-mt_Yw27nweoTj source: https://lightmysky.com/learn/mathematics/reading-solutions-from-a-graph-mt_Yw27nweoTj.md retrieved: 2026-09-02 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Reading solutions from a graph Use graphs of linear and quadratic functions to estimate output values for given inputs, find approximate solutions to equations, and interpret graphical information in real-world contexts Subject: Mathematics · Area: Algebra · Ages 13 to 14 Page: https://lightmysky.com/learn/mathematics/reading-solutions-from-a-graph-mt_Yw27nweoTj ## Ready when they can - Read off an approximate y-value for a given x from a plotted curve - Find approximate solutions to an equation by identifying where a graph crosses the x-axis or another line - Interpret a real-world graph (e.g., distance–time) to answer contextual questions ## Lesson: Reading answers off a graph Not every problem needs algebra. If you have a graph of a line or a curve, you can often read off a good estimate of the answer just by looking at it. A graph reading is an estimate, not an exact answer, so check it against the equation when you need precision. You can only read from the part that is actually plotted: outside that range there is no line to read. **Example.** A graph shows the line y = 2x + 1. To estimate y when x = 3, find x = 3 on the horizontal axis, go straight up to the line, then look across to the y-axis. The line sits at about y = 7 there, so y is approximately 7 when x = 3. *(drawing: Find x = 3 on the bottom axis, go straight up to the line, then read across. The y-axis reading lands at about 7.)* **Example.** A curve for y = x squared minus 4 crosses the x-axis at about x = -2 and x = 2. Those crossing points are where y = 0, so they are the approximate solutions to x squared minus 4 = 0. Two graphs crossing each other works the same way. Where y = x + 3 meets y = 9 - x, both sides have the same value, so that x is the approximate solution to x + 3 = 9 - x. **Example.** A distance-time graph shows a car's distance from home over time. If the line is flat between minute 10 and minute 15, the car is not moving during that time. A line going up means the distance is growing, and a line going down means the car is heading back towards home. How steep the line is tells you the speed, not which way it slopes. **Recap.** A graph lets you estimate an output for a given input, or estimate a solution where two lines or a curve and the x-axis cross. ## Practice 17 questions on this page, each with its working shown. ## Needs first - [Plotting Linear Graphs](https://lightmysky.com/learn/mathematics/plotting-linear-graphs-mt_-3udyo6VyB) - [Quadratic Graphs](https://lightmysky.com/learn/mathematics/quadratic-graphs-mt_GZuoYaDdWd)