Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

In this lesson, the slope of a line segment connecting two point will be measured and a general formula for finding the slope will be developed and used. The line segment shown below connects the points (1, 2) and (3, -2). As we look at this diagram from left to right, the segment slopes downward. We will define a negative number to describe the downward slope and how steeply this line ...

Answer (1 of 2): Start with the slope-intercept form, y=mx+b. We know what the slope is. Can we find what b is? We are given a point (x_1, y_1) on the line. Plug these into the equation: y_1=mx_1+b And solve for b: b = y_1-mx_1. Now put this back in the slope intercept formula where b was....m=. Where m is the slope of the line. The numerical value for slope can be expressed as a ratio or fraction. The numerator will contain the difference of y-values, and the denominator will contain the difference of x-values. The above slope formula is conceptually defined as the rise overrun.