Question

What is the y-intercept of the line thaf passes through the points (3, 7) and (-2, -3)

A.) (1,0)

B.) (0,4)

C.) (0,1)

D.) (0, -4)

Answer 1

So to answer this question you first need to find the point slope form and then convert that to slope intercept form.

Point slope form is y-y1 = m(x-x2) where m is slope and (x2,y2) is a point on the line.
Slope is equal to (y2-y1)/(x2-x1). Since you are given two points you simply plug them in!

(7 - - 3)/(3 - - 2) Cancel the double negatives
(7+3)/(3+2) Add what's in parentheses
10/5 Divide
m = 2

Now you can choose either given point to use in your point slope formula. I will be using (3,7) because I wont have to worry about canceling out the negatives.

y - 7 = 2(x - 3)

Now you simply distribute and isolate y to get slope intercept form.

y-7 = 2(x-3) Distribute the 2

y - 7 = 2x - 6 Add 7 to both sides

y = 2x + 1

Since y = mx+b and b is the y intercept. You that you y value when x is zero is 1. This means your final coordinate will be (0,1) or C.