Write the slope-intercept form of the equation of the line through (0,2) and (1,-3)

y = -5x + 2

Step-by-step explanation:

Label the points that are given.

(0,2) = (x1, y1)

(1, -3) = (x2, y2)

Step 1:  Find the slope, denoted m

This is done by using the formula m = (y2 - y1)/(x2 - x1)

The slope for this problem is

   m = (-3 - 2)/(1 - 0)  

        m = -5/1 = -5

Step 2: The general form for a linear equation in slope-intercept form is

   y = mx + b        where m is the slope and b is the y-intercept

Use what we know about our line to solve the rest.  By using one of the given points, we have 3 of the 4 variables in the above equation.  Pick either point, it doesn't matter which one.  We'll use (0, 2), which is (x, y), and we know that

m = 5

The equation becomes...

  2 = -5(0) + b                      (now solve for b)

   2 = b                                 (  -5(0) = 0

Plug that value into the general form...

y = -5x + 2