Reading a linear relation graph means identifying its y-intercept, where the line crosses the y-axis, and its slope, how steeply it rises or falls. Learn to find both features from a graph and use them to write the line's equation in y = mx + b form.
What to look for on a linear graph
Reading a linear relation graph means pulling out two key features: the y-intercept, where the line crosses the y-axis, and the slope, how steeply the line rises or falls.
Finding the y-intercept
The y-intercept is the point where x = 0. For the line y = 2x + 3, substituting x = 0 gives y = 3, so the line crosses the y-axis at (0, 3).
The y-intercept (0, 3) and a rise-over-run triangle showing a slope of 2.
Finding the slope
Starting from the y-intercept, move 1 unit right; the line rises 2 units to reach (1, 5). That rise-over-run of 2/1 = 2 is the slope — the same rate of change you'd get from any two points on the line.
Reading the equation from the graph
Once you have the y-intercept (b) and the slope (m), you can write the line's equation directly as y = mx + b. This is the reverse of building a table of values from an equation, and the same reading skill applies to solving linear equations once you know a graph's key points.