Write the slope-intercept form of the equation through (-4,0) and (1,5)

y = x + 4

Step-by-step explanation:

Label the points that are given.

(-4, 0) = (x1, y1)

(1, 5) = (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 = (5 - 0)/(1 -  -4)  

        m = 5/5 = 1

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 (-4, 0), which is (x, y), and we know that m = 1

The equation becomes...

  0 = -4(1) + b                      (now solve for b)

   0 = -4 + b                                

            4 = b                            (add  to both sides)

Plug that value into the general form...

y = x + 4