Question

parallel lines model
what line is parallel to $3x + 2y = 6$?

a. $y = -\frac{1}{3}x - 5$
b. $y = \frac{1}{3}x + 6$
c. $y = -\frac{3}{2}x + 2$
d. $y = \frac{2}{3}x - 3$
e. $y = 3x - 15$

Explanation:

Step1: Convert to slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope. We start with the equation $3x+2y = 6$.
Subtract $3x$ from both sides: $2y=-3x + 6$.
Divide each term by 2: $y=-\frac{3}{2}x + 3$. The slope of the given line is $m =-\frac{3}{2}$.

Step2: Find the slope of each option

• Option a: For $y =-\frac{1}{3}x-5$, the slope $m=-\frac{1}{3}$.
• Option b: For $y=\frac{1}{3}x + 6$, the slope $m=\frac{1}{3}$.
• Option c: For $y =-\frac{3}{2}x+2$, the slope $m =-\frac{3}{2}$.
• Option d: For $y=\frac{2}{3}x-3$, the slope $m=\frac{2}{3}$.
• Option e: For $y = 3x-15$, the slope $m = 3$.

Parallel lines have the same slope. So the line with the same slope as $3x + 2y=6$ (slope $-\frac{3}{2}$) is the line in option c.

Answer:

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