Write the slope-intercept form with the points (x_1,y_1) and (x_2,y_2) substituted into the equation.
See solution.
Practice makes perfect
Let's begin by looking at a generic straight line, one that we know can be written in slope-intercept form,
y=mx+b,
but we do not know the values of the slope or the y-intercept. Two points on this line can then be labeled as (x_1,y_1) and (x_2,y_2). The equations of the line expressed using these points are then:
&( x_1, y_1) ⇒ y_1=m x_1+b
&( x_2, y_2) ⇒ y_2=m x_2+bWe can see their relationship in the graph below.
The Slope Formula is
Slope=y_2-y_1/x_2-x_1.
We can substitute the expressions from the previously stated equations for y_1 and y_2 into the Slope Formula to prove the slope equals m.
