Slope-Intercept Form (y = mx + b)
The equation y = mx + b directly tells you a line’s slope (m) and its y-intercept (b).
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The equation y = mx + b is called slope-intercept form because it directly names two key features of the line. Once you know what m and b each mean, you can read a graph from an equation — or write an equation from a graph — without guessing.
The y-intercept (b) is where the line crosses the y-axis; because the y-axis is where x = 0, it is always the point (0, b). The slope (m) describes how steep the line is and its direction: a positive slope rises from left to right, a negative slope falls.
To write the equation of a line from two points, first calculate the slope, then substitute the slope and one point into y = mx + b and solve for b. Lines in standard form Ax + By = C convert by isolating y.
Worked example
Write the equation of the line through (1, 3) and (3, 7).
- Calculate the slope: m = (7 − 3) / (3 − 1) = 4 / 2 = 2.
- Substitute m = 2 and the point (1, 3) into y = mx + b: 3 = 2(1) + b.
- Solve for b: 3 = 2 + b, so b = 1.
- Check with the second point: y = 2(3) + 1 = 7.
y = 2x + 1
On the test: On the GED & HiSET, y = mx + b connects a line’s equation, its table of values, and its graph.
This concept also comes up in Graphing.
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