What does y=mx mean? Where does it come from?

In this lesson you will learn to derive the equation y=mx by

using similar triangles.

Let’s ReviewLet’s Review

For any line, the ratio of rise to run is

constant.

We call this ratio the slope of the

line.

4

6

6

9

Slope = = =

Let’s ReviewA Common Mistake

Be careful!

Slope = Slope =

Let’s ReviewCore Lesson

Slope:

(0, 0)2

3 (x, y)yx

=

y = x

Let’s ReviewCore Lesson

Slope: m

(0, 0)m

1 (x, y)yx

=

y = mx

Let’s ReviewCore Lesson

Any point (x,y) on a line through the origin with slope m will satisfy y=mx.

y=mx is the equation of a line through the origin with slope m.

In this lesson you have learned to derive the equation y=mx

by using similar triangles.

Let’s ReviewGuided Practice

Use similar triangles to demonstrate that the equation of a line through the origin with slope 3 is y=3x.

Let’s ReviewExtension Activities

A line through the origin has slope . Does it pass through (8,10)? Explain.

Let’s ReviewExtension Activities

A line through the origin passes through (5,6). What is the line’s equation?

Let’s ReviewQuick Quiz

Use similar triangles to demonstrate that the equation of a line through the origin with slope is y= x.