Final answer:
To convert the equation 1/4y = 2x - 2y into slope-intercept form, you multiply both sides by 4, add 8y to both sides, and then divide by 9, resulting in y = 8/9x. The slope is 8/9 and the y-intercept is zero.
Step-by-step explanation:
To convert the equation 1/4y = 2x - 2y into slope-intercept form, you first need to manipulate the equation so it is in the form of y = mx + b, where m is the slope and b is the y-intercept.
We begin by isolating y on one side of the equation:
- Multiply both sides by 4 to get rid of the fraction:
4(1/4y) = 4(2x - 2y) - Simplify:
y = 8x - 8y - Move all terms involving y to one side by adding 8y to both sides:
9y = 8x - Divide both sides by 9 to solve for y:
y = 8/9x
Now, the equation is in slope-intercept form, with the slope (m) being 8/9 and the y-intercept (b) is zero since there is no constant term on the right side of the equation.