Final answer:
The slope-intercept form of the equation 6x+5y=-15 is y = (-6/5)x - 3, where -6/5 is the slope and -3 is the y-intercept.
Step-by-step explanation:
To write the equation 6x+5y=-15 in slope-intercept form, we need to solve for y to get it into the form y = mx + b, where m is the slope and b is the y-intercept.
Here are the steps to rewrite the equation:
- Move the term with x to the other side: 5y = -6x - 15.
- Divide every term by the coefficient of y, which is 5: y = (-6/5)x - 3.
In this equation, -6/5 is the slope, and -3 is the y-intercept, which means the line falls 6 units on the vertical axis for every 5 units it moves to the right on the horizontal axis, and it intersects the y-axis at (0, -3).