Question

What is the y-coordinate fo the y-intercept of the line that passes through the points (-4,-4) and (4,8)

Answer 1

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:  $m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

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.

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m = \frac{8-(-4)}{4-(-4)}$     Simplify the numerator and denominator

$m = \frac{12}{8}$     Reduce the fraction. Top and bottom can divide by 4.

$m = \frac{3}{2}$     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.

Substitute a random point (4,8) and the slope (3/2) into the equation. Then isolate "b" to find the y-intercept.

$y = mx + b$

$8 = (\frac{3}{2})(4) + b$     Multiply 3/2 and 4 by combining into the numerator

$8 = \frac{3*4}{2} + b$     Simplify the fraction. 12/2 = 6

$8 = 6 + b$     Isolate "b"

$8 - 6 = b$     Subtract 6 from both sides

$b = 2$     Write variable on left side for standard formatting.

Therefore the y-coordinate for the y-intercept of the line is 2.

Answer 2

If you see the slope intercept form that’s the y coordinate