Question

Translate the equation 6x - 3y = 12 into slope-intercept form and state the slope and y-intercept.

A. y = 2x + 4; Slope = 2, Y-intercept = 4
B. y = -2x - 4; Slope = -2, Y-intercept = -4
C. y = 2x - 4; Slope = 2, Y-intercept = -4
D. y = -2x + 4; Slope = -2, Y-intercept = 4

Answer 1

The slope-intercept form of the equation 6x - 3y = 12 is y = 2x - 4, which means the slope is 2 and the y-intercept is -4.

Step-by-step explanation:

To translate the equation 6x - 3y = 12 into slope-intercept form and state the slope and y-intercept, we first need to isolate the y-variable on one side of the equation. We do this by first subtracting 6x from both sides, and then dividing each term by -3, which results in the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.

So after the manipulation, the equation will look like this:

-3y = -6x + 12

y = 2x - 4

Therefore, the slope of the line is 2 and the y-intercept is -4. This matches option C, which states y = 2x - 4; Slope = 2, Y-intercept = -4.