Question

Which linear equation represents the same relationship shown in the graph Below?

Answer 1

Notice that the y-intercept of the line in the graph is 5. Set x=0 on the given equations to find which of them satisfy that condition. It turns out that there are two possibilities:

`y=-(2)/(5)x+5`
`y=-(5)/(2)x+5`

Furthermore, we can see that when x=2, then y=0 on the graph. substitute x=2 on those equations to find which of them satisfy that condition:

`\begin{gathered} y=-(2)/(5)(2)+5 \\ =-(4)/(5)+5 \\ =4.2 \end{gathered}`
`\begin{gathered} y=-(5)/(2)(2)+5 \\ =-5+5 \\ =0 \end{gathered}`

Then, the equation:

`y=-(5)/(2)x+5`

is the only one which matches the line on the image.