Final answer:
The slope of the line 4x + 3y = -24 is -4/3, found by rearranging the equation to the slope-intercept form y = (-4/3)x - 8.
Step-by-step explanation:
To find the slope of the line given by the equation 4x + 3y = -24, we first need to write the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. By rearranging the given equation, we subtract 4x from both sides to get 3y = -4x - 24. Next, we divide every term by 3 to solve for y, obtaining y = (-4/3)x - 8. In this form, we can see that the coefficient of x is the slope of the line.
Therefore, the slope of the line described by the equation 4x + 3y = -24 is -4/3. This means that for every increase of 1 unit on the horizontal axis (x), there is a decrease of 4/3 units on the vertical axis (y).