Question

Write the equation of a line (in slope /intercept form) that is parallel to -2x + 4y = 100 and goes through the (8, -7)

Answer 1

Answer:

y = ½x - 11

Step-by-step 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