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
What a learner can do afterwards
- 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
1 · Read
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.
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.
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.
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.
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.
2 · Watch
Take it off screen
Where it sits
Learn first
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Nothing builds on it yet.
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.