Answer:
y = 2
Step-by-step explanation:
Because we need to find the y-intercept, we should find the equation of the line in slope-intercept form (y = mx + b).
"x" and "y" represent a point on the line.
"m" represents the slope (how steep the line is).
"b" represents the y-intercept (where the line hits the y-axis).
Given the two coordinates on the line, use the formula to find slope: [tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
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.
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m = \frac{8-(-4)}{4-(-4)}[/tex] Simplify the numerator and denominator
[tex]m = \frac{12}{8}[/tex] Reduce the fraction. Top and bottom can divide by 4.
[tex]m = \frac{3}{2}[/tex] 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.
Substitute a random point (4,8) and the slope (3/2) into the equation. Then isolate "b" to find the y-intercept.
[tex]y = mx + b[/tex]
[tex]8 = (\frac{3}{2})(4) + b[/tex] Multiply 3/2 and 4 by combining into the numerator
[tex]8 = \frac{3*4}{2} + b[/tex] Simplify the fraction. 12/2 = 6
[tex]8 = 6 + b[/tex] Isolate "b"
[tex]8 - 6 = b[/tex] Subtract 6 from both sides
[tex]b = 2[/tex] Write variable on left side for standard formatting.
Therefore the y-coordinate for the y-intercept of the line is 2.
