Question

Which equation could represent the relationship shown in the scatter plot?

A. y=3x
B. y=5/2x-1
C. y=1/2x+7
D. y= -x+8

Answer 1

`y=(1)/(2)x+7`

Explanation:

Let's analyze each case.

case A)
`y=3x`

This equation represent a direct variation and the relationship shown in the scatter plot does not passes through the origin

therefore

The equation case A) could not represent the relationship shown in the scatter plot

case B)
`y=(5)/(2)x-1`

The y-intercept of this equation is equal to
`-1` and the relationship shown in the scatter plot does not have points with negative y-coordinates

therefore

The equation case B) could not represent the relationship shown in the scatter plot

case C)
`y=(1)/(2)x+7`

The y-intercept of this equation is equal to
`7` and the relationship shown in the scatter plot has points with nearest coordinates

therefore

The equation case C) could represent the relationship shown in the scatter plot

case D)
`y=-x+8`

This equation has a slope negative and the relationship shown in the scatter plot has a positive slope

therefore

The equation case D) could not represent the relationship shown in the scatter plot

Answer 2

From the scatter plot, the equation that could represent the relationship shown is y = 1/2x + 7.