Question
How would you write the equation of a line that would be parallel to y = -3x -2, but not share any points. * 1 point
y = 3x - 2
y = -3x - 2
y = 3x + 8
y = -3x + 8
y = 3x - 2
y = -3x - 2
y = 3x + 8
y = -3x + 8
Answers
GPT-4o mini
To write the equation of a line that is parallel to \( y = -3x - 2 \), we need to keep the same slope, which is \(-3\), but it must have a different y-intercept to ensure it does not share any points with the original line.
The equation of a line in slope-intercept form is given by:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept. Since we want the slope to remain \(-3\), we can write the equation as:
\[ y = -3x + b \]
Now, to make sure the new line does not share any points with the original line, we need to choose a different y-intercept \( b \) from the one in the original equation, which is \(-2\).
Looking at the options you provided, we can choose the equation \( y = -3x + 8 \), where the slope is \(-3\) and the y-intercept is \(8\), which is different from \(-2\).
Thus, the correct answer is:
**y = -3x + 8**
The equation of a line in slope-intercept form is given by:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept. Since we want the slope to remain \(-3\), we can write the equation as:
\[ y = -3x + b \]
Now, to make sure the new line does not share any points with the original line, we need to choose a different y-intercept \( b \) from the one in the original equation, which is \(-2\).
Looking at the options you provided, we can choose the equation \( y = -3x + 8 \), where the slope is \(-3\) and the y-intercept is \(8\), which is different from \(-2\).
Thus, the correct answer is:
**y = -3x + 8**