Answer:
y = ½x - 11
Explanation:
The equation of the line that goes through (8, -7) and is parallel to -2x + 4y = 100, will have the same slope as the line, but different y-intercept (b).
Let's find the slope of -2x + 4y = 100 by rewriting in the slope-intercept form.
-2x + 4y = 100
Add 2x to both sides
4y = 2x + 100
Divide both sides by 4
y = 2x/4 + 100/4
y = ½x + 25
The slope of the given line is ½. Since the line that goes through (8, -7) is parallel to -2x + 4y = 100, therefore the slope (m) is also ½.
To find the y-intercept (b), substitute m = ½, x = 8, and y = -7 into y = mx + b.
-7 = ½(8) + b
-7 = 4 + b
-7 - 4 = b
-11 = b
b = -11
Substitute m = ½ and b = -11 into y = mx + b to get the equation of the line that is parallel to -2x + 4y = 100.
y = ½x + (-11)
y = ½x - 11