Slope and Intercepts of a Line

Slope Intercept Form

A line is written as y equals m times x plus b, where m is the slope and b is the y intercept. Two numbers fully determine a straight line, so any two distinct points on a line determine its equation.

Finding the Intercept

Set x to zero in the equation. Then y equals b, which is the y intercept. For the line through 0,1 and 1,3 the slope is 2 and substituting the first point gives b equals 1.

Finding the x Intercept

Set y to zero and solve for x. For y equals 2x minus 4, setting y to zero gives x equals 2, so the line crosses the x axis at the point 2, 0.

Lines With No Intercept

A vertical line has no slope and no y intercept, and is written as x equals a constant. A horizontal line at y equals 4 has a slope of zero and crosses the y axis, but never crosses the x axis at all.

Slope Intercept Against Point Slope Form

Point slope form, y minus y1 equals m times x minus x1, is often easier since it uses a point you already have. Converting to slope intercept form by expanding gives the y intercept directly.

The Angle of Inclination

The angle the line makes with the x axis is the arctangent of the slope. Slopes of 1, the square root of 3 and infinity correspond to angles of 45, 60 and 90 degrees, which are the angles of the equilateral triangle.