Final answer:
The equation of a line that crosses the x-axis at x = -4 with a negative slope is given by option (C) y = -5x + 20, which is the only equation that meets both criteria.
Step-by-step explanation:
When determining the equation of a line that crosses the x-axis at a specific point and has a certain slope, we should look for two characteristics in the equation: the x-intercept and the slope. The x-intercept is the value of x where the line crosses the x-axis, and the slope indicates the steepness of the line and whether it rises or falls as it moves from left to right on a graph.
In this case, we are looking for a line that crosses the x-axis when x = -4 and has a negative slope. A negative slope means that as we move from left to right, the line goes downward. Given these criteria, let's evaluate the options provided:
- (A) y = 5x + 20: This has a positive slope and is therefore not correct.
- (B) y = -5x - 20: This has a negative slope, but it would cross the x-axis at x = 4, not x = -4.
- (C) y = -5x + 20: This option has a negative slope and crosses the x-axis at x = -4 because if you set y=0 to find the x-intercept, x indeed equals -4. Thus, this is the correct equation.
- (D) y = 5x - 4: Positive slope, incorrect.
- (E) y = -5x - 4: Negative slope but incorrect x-intercept.
Therefore, the correct option, based on the given information, is (C) y = -5x + 20.