Which equation of a line is parallel to the equation -4x + 3y = 12?
Responses
y = 4x + 8
y = 4x + 8
y = 3x + 12
y = 3x + 12
y =43x + 6
y =43x + 6
y=−43x + 4
To find the equation of a line parallel to the given line -4x + 3y = 12, we first need to put the given equation in slope-intercept form (y = mx + b), where m is the slope of the line.
Rearrange the given equation to solve for y:
-4x + 3y = 12
3y = 4x + 12
y = (4/3)x + 4
Now that the equation is in slope-intercept form, we can see that the slope (m) of the line is (4/3). Parallel lines have the same slope, so we need to find an equation that has the slope of (4/3) as well.
Let's analyze the options provided:
y = 4x + 8
The slope here is 4, which is not equal to (4/3), so this line is not parallel to the given line.
y = 3x + 12
The slope here is 3, which is not equal to (4/3), so this line is not parallel to the given line.
y = (4/3)x + 6
The slope here is (4/3), which is equal to the slope of the given line, making this line parallel to the given line.
y = −(4/3)x + 4
The slope of this line is −(4/3), which is the negative reciprocal of the given line's slope, which means this line is perpendicular, not parallel, to the given line.
Therefore, the equation y = (4/3)x + 6 is the correct option, as it is the only line whose slope is equal to (4/3), the same as the slope of the line given by the equation -4x + 3y = 12.