Final answer:
To find the slope and y-intercept from the equation 9y-3x=18, divide all terms by 9 to arrange it into the slope-intercept form y = mx + b. This will yield y = (1/3)x + 2, indicating a slope (m) of 1/3 and a y-intercept (b) of 2.
Step-by-step explanation:
To convert the given equation 9y-3x=18 into slope-intercept form, we first need to solve for y. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.
First, we'll isolate y on one side of the equation:
- Divide every term in the equation by 9 to get y by itself:
- Simplify the equation:
- y = (1/3)x + 2
The slope m is 1/3, which means there is a rise of 1 on the vertical axis for every increase of 3 on the horizontal axis. The y-intercept b is 2, the point where the line intersects the y-axis.