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Wednesday 29th of June
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 Dependent Variable

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# Slope-Intercept Form of a Line

The line y = -3x - 1 has slope -3. To find the y-intercept of this line, let x = 0 in y = -3x - 1: y = -3(0) - 1 = -1. The y-intercept is (0, -1). Its y-coordinate appears in the equation:

Because the slope and y-intercept can be read from the equation when it is solved for y, this form of the equation of the line is called slope-intercept form.

Slope-Intercept Form

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and (0, b) is the y-intercept.

Example 1

Writing an equation given its slope and y-intercept

Write the slope-intercept form of the equation of the line shown in the figure below.

Solution

From the figure we see that the y-intercept is (0, 3). If we start at the y-intercept and move down 2 and 3 to the right, we get to another point on the line. So the slope is . The equation of this line in slope-intercept form is