Question

Which set of points includes all of the solutions for (y = 5/2x + 3/2), line going through (-1, -1) and (1, 4)?

a. ((-1, -1), (0, 1.5), (1, 4))
b. ((-3, -6), (-2, -3.5), (0, 1.5), (2, 6.5), (3, 9))
c. ((-1, -1), (1, 4))
d. ((-3, -6), (0, 1.5), (3, 9))

Answer 1

The set of points that includes all solutions for the line y = 5/2x + 3/2, which goes through (-1, -1) and (1, 4), is option a: ((-1, -1), (0, 1.5), (1, 4)), because each point satisfies the line equation.

Step-by-step explanation:

To solve the question which set of points includes all of the solutions for the line (y = 5/2x + 3/2) that goes through the points (-1, -1) and (1, 4), we need to test which sets of points satisfy the equation.

For option a, plugging in (-1, -1), we get:
y = 5/2*(-1) + 3/2
y = -5/2 + 3/2
y = -2/2
y = -1

This verifies that (-1, -1) is on the line. Next, for (0, 1.5), we have:
y = 5/2*0 + 3/2
y = 3/2
y = 1.5

This also lies on the line. Finally, for (1, 4), we have:
y = 5/2*(1) + 3/2
y = 5/2 + 3/2
y = 8/2
y = 4

Therefore, option a, with the points ((-1, -1), (0, 1.5), (1, 4)), correctly represents all the solutions given the provided line equation.