Question

Using the graph below, which of the following equations represents the line that is parallel to line FG and passes through the (8, - 3) point?

Answer 1

Answer:

$y = -\frac{7}{4}x + b$

Explanation:

The equation if the line that is parallel to line FG, will have the same slope as line FG.

To find that equation in slope-intercept intercept form, y = mx + b, we need to find m (slope) and b (y-intercept).

The slope, m, will be the same as the slope of line FG.

Let's calculate the slope of line FG:

F(-4, -2) and G(-8, 5)

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 -(-2)}{-8 -(-4)} = \frac{7}{-4}$

The slope, m, of the line that is parallel to line FG will be -⁷/4.

Substitute x = 8, y = -3, m = -⁷/4 into y = mx + b and solve for the y-intercept, b, of the equation if the line that is parallel bro line FG.

$-3 = -\frac{7}{4}(8) + b$

$-3 = -\frac{7}{1}2 + b$

$-3 = -14 + b$

Add 14 to both sides

$-3 + 14 = b$

$11 = b$

$b = 11$

Substitute m = -⁷/4 and b = 11 into y = mx + b

$y = -\frac{7}{4}x + b$

Therefore, the equation that represents the line that is parallel to line FG and passes through the (8, - 3) point is $y = -\frac{7}{4}x + b$.