Question

Which set of ordered pairs (x,y) could represent a linear function?A. {(-7,3), (-2,1), (3,-1), (8,-3)}B. {(-2,8), (-1,4), (1,0), (3,-4)}C. {(-3,-6), (0,-5), (3,-3) (6,-2)}D. {(0,-8), (3,-5), (5,-2), (8,1)}

Answer 1

A. {(-7,3), (-2,1), (3,-1), (8,-3)}

Step-by-step explanation:

A linear function has a constant slope.

To determine the set of ordered pairs (x,y) that could represent a linear function, we find the slope for two pairs of points.

`\text{Slope}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}`

Option A

Using points (-7,3) and (-2,1).

`\text{Slope}=(3-1)/(-7-(-2))=(2)/(-7+2)=-(2)/(5)`

Using points (-7,3) and (3,-1).

`\text{Slope}=(3-(-1))/(-7-3)=(4)/(-10)=-(2)/(5)`

We see that the slopes are the same.

Therefore, the set of ordered pairs in Option A represent a linear function.