The slope intercept form

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Question from Dave, a student:

Hi, why is there a y-intercept in the slope intercept form? What does the y-intecept have to do with the equation?

Hi Dave,

Suppose I am thinking about a line and its slope is -2. Here are some possibilities.

lines

How can I tell you which line I am thinking about? I am going to tell you which one with an equation that I produce using the point (0, 5) where the line crosses the y-axis. Suppose (x, y) is some other point on the line. Since the slope of the line is -2 the slope of the line joining (0, 5) and (x, y) is -2. That is

If I now multiply both sides by x I get

y - 5 = -2x or y = -2x + 5.

This is exactly the slope intercept form of the line, the slope is -2 and the y-intercept is 5.

I hope this helps,
Penny

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