Write the equation of the line that passes through (1,5) and (-2,14) in slope-intercept form.

y=3x+2
y=3x+8
y=-3x-2
y=-3x+8

First the slope m

m=14-5/-2-1
m=9/-3
m=-3

y=-3x+b
5=-3 (1)+b
5=-3+b
8=b

y=-3x+8 the answer is D

Slope-intercept form:
y=mx+b
m=slope
b=intercept form

Given two points (x₁,y₁) and (x₂,y₂), the slope of the line passes through these points will be:
m=(y₂-y₁)/(x₂-x₁)

In this case, the points are (1,5) and (-2,14), then the slope will be:
m=(14-5)/(-2-1)=9/(-3)=-3

therefore, the equation will be:
y=-3x+b
we need to know the value of b; Therefore, we can use any known point of this line [  (1,5)    or (-2,14)] . The result will be the same. 
For example:
Point (1,5);     ⇒ when    x=1; then  y=5

y=mx+b
5=-3(1)+b
5=-3+b
b=5+3
b=8

Now, we know the slope (m=-3) and y-intercept (b=8), therefore the equation of this line will be.

y=-3x+8

y=-3x+8