Answer:
y = 2
Step-by-step explanation:
Because we need to <u>find the y-intercept</u>, we should find the equation of the line in <u>slope-intercept form</u> (y = mx + b).
"x" and "y" represent a point on the line.
"m" represents the slope (how steep the line is).
<u>"b" represents the y-intercept</u> (where the line hits the y-axis).
Given the two coordinates on the line, <u>use the formula to find slope</u>:   
 
Choose which point will be point 1 and point 2. Remember points are written (x, y).
Point 1 (-4, -4)    x₁ = -4   y₁ = -4
Point 2 (4, 8)     x₂ = 4    y₂ = 8
Substitute the information from the coordinates into the slope formula.

 Simplify the numerator and denominator
     Simplify the numerator and denominator
 Reduce the fraction. Top and bottom can divide by 4.
     Reduce the fraction. Top and bottom can divide by 4.
 Slope of the line, m = 3/2
     Slope of the line, m = 3/2
Since we know at least one point on the line and the slope, we only have one missing piece of information in the equation y = mx + b.
<u>Substitute a random point</u> (4,8) <u>and the slope</u> (3/2) into the equation. Then <u>isolate "b" to find the y-intercept</u>.

 Multiply 3/2 and 4 by combining into the numerator
     Multiply 3/2 and 4 by combining into the numerator
 Simplify the fraction. 12/2 = 6
     Simplify the fraction. 12/2 = 6
 Isolate "b"
     Isolate "b"
 Subtract 6 from both sides
     Subtract 6 from both sides
 Write variable on left side for standard formatting.
     Write variable on left side for standard formatting.
Therefore the y-coordinate for the y-intercept of the line is 2.