Question

Write another set of equations with the same relationship as y = 2x - 5, y = 2x, and y = 2x + 4.

a) y = 3x - 7, y = 3x, y = 3x + 5
b) y = x - 2, y = x, y = x + 2
c) y = 4x - 8, y = 4x, y = 4x + 8
d) y = 2x + 3, y = 2x, y = 2x - 3

Answer 1

Option (a) with equations y = 3x - 7, y = 3x, and y = 3x + 5 is the correct set that maintains the same relationship as the original equations, with a constant slope and differing y-intercepts.

Step-by-step explanation:

The given equations y = 2x - 5, y = 2x, and y = 2x + 4 have a consistent relationship: each equation has the same slope but different y-intercepts. To write another set of equations with the same relationship, we need to choose a constant slope for all three but alter the y-intercept appropriately.

From the options provided, the correct set of equations is (a) y = 3x - 7, y = 3x, and y = 3x + 5. Here, each equation has a slope of 3, and the y-intercepts are -7, 0, and 5, respectively, mirroring the structure of the original set of equations where the slope is constant (2 in that case).