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=-\frac{2}{5}x+5$$y=-\frac{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=-\frac{2}{5}(2)+5 \\ =-\frac{4}{5}+5 \\ =4.2 \end{gathered}$$\begin{gathered} y=-\frac{5}{2}(2)+5 \\ =-5+5 \\ =0 \end{gathered}$

Then, the equation:

$y=-\frac{5}{2}x+5$

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