Determine the intercepts of the line that passes through the following points. (-15,5) (-9,10) (-3,15)

To find the x and y-intercept, we can write an equation in slope intercept form. 
first, we need to find the slope
the formula for slope is 
m= (y₂-y₁)/(x₂-x₁)

now just put any two points into the equation
m=(10-5)/(-9-(-15)
m=5/6

so now we can write the slope-intercept equation
y=5/6x + b

in a slope-intercept equation, b is equal to the y-intercept, so we can take one of our 3 pairs of points and put them into the equation to solve for b

15= 5/6(-3) +b
15=-2.5 + b
17.5 = b
so now we know the y-intercept is (0,17.5)

now we can write the equation as 
y= 5/6x + 17.5

since the x intercept is when y=0, we can set y to 0 and then solve for x

0= 5/6x +17.5
-17.5 = 5/6x
-21 = x 

by setting y to zero, we figured out that the x-intercept is (-21,0)

hope this helped!