Question
The slope of which of the following is PARALLEL to the equation -2x +6y =6? Hint: It would be helpful to get the equation in y=mx +b form or try graphing (1 point) Responses 1/3 -3/2 -1/3 3/2
Answers
Answered by
GPT-4o mini
To determine the slope of the equation \( -2x + 6y = 6 \), we first need to rewrite it in the slope-intercept form \( y = mx + b \), where \( m \) represents the slope.
Starting with the original equation:
\[
-2x + 6y = 6
\]
First, we isolate \( y \):
1. Add \( 2x \) to both sides:
\[
6y = 2x + 6
\]
2. Divide every term by \( 6 \):
\[
y = \frac{2}{6}x + \frac{6}{6}
\]
\[
y = \frac{1}{3}x + 1
\]
Now, we can see that the slope \( m \) of the equation \( y = \frac{1}{3}x + 1 \) is \( \frac{1}{3} \).
For a line to be parallel to another line, it must have the same slope. Therefore, we are looking for a slope that is equal to \( \frac{1}{3} \).
Among the given options, the slope that is parallel to the original equation is:
**1/3**.
Starting with the original equation:
\[
-2x + 6y = 6
\]
First, we isolate \( y \):
1. Add \( 2x \) to both sides:
\[
6y = 2x + 6
\]
2. Divide every term by \( 6 \):
\[
y = \frac{2}{6}x + \frac{6}{6}
\]
\[
y = \frac{1}{3}x + 1
\]
Now, we can see that the slope \( m \) of the equation \( y = \frac{1}{3}x + 1 \) is \( \frac{1}{3} \).
For a line to be parallel to another line, it must have the same slope. Therefore, we are looking for a slope that is equal to \( \frac{1}{3} \).
Among the given options, the slope that is parallel to the original equation is:
**1/3**.