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Alik [6]
3 years ago
13

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

Mathematics
2 answers:
Sedbober [7]3 years ago
8 0

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>:  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.

<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>.

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.

podryga [215]3 years ago
4 0
If you see the slope intercept form that’s the y coordinate

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