Final answer:
To convert 3x - 5y - (-2) = 15 into slope-intercept form, subtract 3x and add 2 on both sides, and then divide every term by -5. The resulting equation will be y = (3/5)x - 13/5, which is in slope-intercept form with a slope of 3/5 and a y-intercept of -13/5.
Step-by-step explanation:
To convert the equation 3x - 5y - (-2) = 15 into slope-intercept form, we follow these steps:
- Move the x-term to the other side by subtracting 3x from both sides to isolate the y-term.
- Add 2 to both sides to eliminate the negative sign in front of the 2.
- Divide every term by -5 to solve for y.
Following these steps, the equation will be transformed as follows:
3x - 5y + 2 = 15
-5y = -3x + 13
y = (3/5)x - 13/5
Now the equation is in slope-intercept form y = mx + b, where m is the slope, and b is the y-intercept. The slope here is 3/5, and the y-intercept is -13/5.