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# Slope-Intercept Form for the Equation of a Line

We have found the equation of a line in point-slope form and in standard form.

Another form for the equation of a line is the slope-intercept form. We can derive this from the point-slope form.

 We begin with the point-slope form for the equation of a line.Use the y-intercept, (0, b), for the point (x1, y1).That is, substitute 0 for x1 and b for y1. y - y1 y - b = m(x - x1) = m(x - 0) Simplify the right side. Add b to both sides. y - b y = mx = mx + b

Definition â€” Slope-Intercept Form for the Equation of a Line

The slope-intercept form for the equation of a line with slope m and y-intercept (0, b) is:

y = mx + b

Example 1

Find the equation of the line with y-intercept (0, -6) and slope 2.

Write the equation in slope-intercept form.

Solution

 Substitute the given values in the slope-intercept form of the equation. Both the slope, m, and the y-intercept, (0, b), are given: m is 2 and b is -6. Simplify. y = mx + b y = 2x + (-6) y = 2x - 6
The slope-intercept form of the equation of the line with y-intercept (0, -6) and slope 2 is y = 2x - 6.

Note â€” To Write the Equation of a Line Given Two Points

Here are two ways to write the equation of a line when given two points:
 Use the Point-Slope Form Step 1 Find the slope. Step 2 Substitute the slope, m, and the coordinates of one of the points, (x1, y1), in y - y1 = m(x - x1) Step 3 Simplify. Use the Slope-Intercept Form Step 1 Find the slope. Step 2 Substitute the slope, m, and the coordinates of one of the points, (x, y), in y = mx + b Then, solve the equation for b. Step 3 Substitute the value of m and the value b in y = mx + b.

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