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

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

Answer 2

y = 2

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 = (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 = (y_(2)-y_(1))/(x_(2)-x_(1))`

`m = (8-(-4))/(4-(-4))` Simplify the numerator and denominator

`m = (12)/(8)` Reduce the fraction. Top and bottom can divide by 4.

`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.

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 = ((3)/(2))(4) + b` Multiply 3/2 and 4 by combining into the numerator

`8 = (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.