Question

Which equation does not belong with the other three?

a) $y=-5x-1$ y is equal to negative 5 x minus 1
b) $2x-y=8$ 2 x minus y is equal to 8
c) $y=x 4$ y is equal to x plus 4
d) $y=-3x 13$ y is equal to negative 3 x plus 13

Answer 1

Equation c, y = x + 4, does not belong with the other three because it is the only equation with a positive slope of 1, making it distinct from the others which have different slopes and y-intercepts.

Step-by-step explanation:

To determine which equation does not belong with the other three, we can look at the characteristics of a linear equation. A linear equation is of the form y = mx + b, where m is the slope and b is the y-intercept. Let's rewrite each equation in this standard format:

• a) y = -5x - 1
• b) y = 2x - 8 (after rearranging 2x - y = 8)
• c) y = x + 4
• d) y = -3x + 13

All four equations are linear, but equations a, b, and d have negative or positive slopes, and their y-intercept values are also integers. However, option c, y = x + 4, stands out because it is the only equation with a positive slope of 1, while the others have negative slopes or a different positive slope. Additionally, c is the only equation where the slope is a simple positive integer, making it the answer that does not belong with the other three.