Question

lesson practice 9a
be sure all the equations are in the slope–intercept form before comparing the slo
may be more than one answer for some of these questions.

1. which of the following lines are parallel to ( y = -3x + 2 )?

a. ( y = \frac{1}{3}x - 2 )
b. ( y = -3x )
c. ( y = 4 - 3x )

Explanation:

Step1: Recall slope-intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Two lines are parallel if and only if their slopes are equal. For the line $y=-3x + 2$, the slope $m_1=-3$.

Step2: Find the slope of option A

For the line $y=\frac{1}{3}x - 2$, comparing with $y = mx + b$, the slope $m_A=\frac{1}{3}$. Since $\frac{1}{3}
eq - 3$, the line in option A is not parallel to $y=-3x + 2$.

Step3: Find the slope of option B

For the line $y=-3x$, comparing with $y = mx + b$, the slope $m_B=-3$. Since $m_B=m_1=-3$, the line in option B is parallel to $y=-3x + 2$.

Step4: Find the slope of option C

First, rewrite the line $y = 4-3x$ in the form $y=mx + b$. We get $y=-3x + 4$. Comparing with $y = mx + b$, the slope $m_C=-3$. Since $m_C=m_1=-3$, the line in option C is parallel to $y=-3x + 2$.

Answer:

B. $Y = - 3X$, C. $Y = 4 - 3X$