Question

Identify an equation in point-slope form for the ine parallel to y = -2/3 x+8 that

Answer 1

Answer:

$y +5 = -\frac{2}{3}(x - 4)$

Step-by-step explanation:

Given

$y = -\frac{2}{3}x + 8$

Point (4,-5)

Required

Determine the line equation

From the question, we understand that the line is parallel to $y = -\frac{2}{3}x + 8$

This implies that they have the same slope, m

A linear equation is:

$y = mx + b$

Where

$m = slope$

By comparison: $y = mx + b$ and $y = -\frac{2}{3}x + 8$

$m = -\frac{2}{3}$

Next, we determine the line equation using:

$y - y_1 = m(x - x_1)$

Where

$(x_1,y_1) = (4,-5)$ and $m = -\frac{2}{3}$

$y - (-5) = -\frac{2}{3}(x - 4)$

$y +5 = -\frac{2}{3}(x - 4)$

Hence,

Option C is correct