Final answer:
Rewriting 3x - 4y = 12 in slope-intercept form gives y = 3/4x - 3, where the slope is 3/4 and the y-intercept is -3.
Step-by-step explanation:
To rewrite the linear equation 3x - 4y = 12 in slope-intercept form, we need to solve for y so that it is expressed in the form y = mx + b, where m is the slope and b is the y-intercept. To do this, we will perform the following steps:
Move the term involving x to the right side of the equation:
-4y = -3x + 12
Divide each term by -4, the coefficient of y:
y = ¾x - 3
In this slope-intercept form, the slope (m) is ¾, which means there is a rise of 3 on the vertical axis for every increase of 4 on the horizontal axis. The y-intercept (b) is -3, indicating that the line crosses the y-axis at the point (0, -3).