Question

question 12 (1 point) which equation has a graph that is a line passing through the point (-3, 7) and is parallel to the graph of y = (2/3)x - 5? a y = (2/3)x + 1 b y = - (3/2)x + 5/2 c y = (2/3)x + 9 d y = (3/2)x + 23/2

Explanation:

Step1: Determine the slope

Parallel lines have the same slope. The given line is \( y = \frac{2}{3}x - 5 \), so the slope \( m = \frac{2}{3} \). So the equation we want has slope \( \frac{2}{3} \), which eliminates options b and d.

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1 = m(x - x_1) \), where \( (x_1,y_1)=(-3,7) \) and \( m=\frac{2}{3} \).
Substitute the values: \( y - 7=\frac{2}{3}(x + 3) \)

Step3: Simplify the equation

Expand the right - hand side: \( y - 7=\frac{2}{3}x+2 \)
Add 7 to both sides: \( y=\frac{2}{3}x + 2+7=\frac{2}{3}x+9 \)

Answer:

c. \( y=\frac{2}{3}x + 9 \)