Final answer:
The equation for the line connecting the points (-1,7.5) and (4,0) is found by first calculating the slope, which is -1.5, and then finding the y-intercept, which is 6, resulting in the equation y = -1.5x + 6 (option a).
Step-by-step explanation:
The equation for the line connecting the points (-1,7.5) and (4,0) can be determined by first calculating the slope of the line and then using one of the points to find the y-intercept. The slope (m) is found using the formula:
m = (y2 - y1) / (x2 - x1)
Here, (x1, y1) = (-1, 7.5) and (x2, y2) = (4, 0), thus:
m = (0 - 7.5) / (4 - (-1)) = -7.5 / 5 = -1.5
The slope-intercept form of a line's equation is y = mx + b. Using the slope m = -1.5 and point (-1, 7.5):
7.5 = (-1.5)(-1) + b
7.5 = 1.5 + b
b = 7.5 - 1.5
b = 6
Therefore, the equation of the line is y = -1.5x + 6, which corresponds to option (a).