Final answer:
To find the slope and y-intercept of the equation 3x-2y=12, solve for 'y' to get the equation in slope-intercept form, yielding a slope of 3/2 and a y-intercept of -6.
Step-by-step explanation:
To find the slope and y-intercept of the straight-line equation 3x-2y=12, you'll first need to solve for y to put it in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Here's a step-by-step process to do this:
- Move the term involving x to the other side by subtracting 3x from both sides of the equation: -2y = -3x + 12.
- Divide each term by -2 to solve for y: y = (3/2)x - 6.
Now your equation is in slope-intercept form. Here, the slope (m) is 3/2, which means that there is a rise of 3 on the vertical axis for every increase of 2 on the horizontal axis. The y-intercept (b) is -6, meaning the point where the line intersects the y-axis is at (0, -6).