Answer:
c. [tex]y=-\frac{2}{3}x+6[/tex]
Step-by-step explanation:
We have to choose that equation which represents the given graph.
From given graph , the graph cut the y- axis at point (0,6) and cut the x- axis (9,0).
a.[tex]y=-2x-6[/tex]
Substitute x=0 then we get
y=-6
But we have y-intercept y=6
Therefore, this equation does not represents the given graph.
b. [tex]y=\frac{2}{3}x+6[/tex]
Substitute y=0 then, we get
[tex]\frac{2}{3}x+6=0[/tex]
[tex]\frac{2}{3}x=-6[/tex]
[tex]x=\frac{-6\times 3}{2}=-9[/tex]
The x- intercept =-9
But , we have x=9
Therefore, it is false.
c. [tex]y=-\frac{2}{3}x+6[/tex]
Substitute x=0 then we get
y=6
Substitute y=0
Then, we get
[tex]-\frac{2}{3}x+6=0[/tex]
[tex]\frac{2}{3}x=6[/tex]
[tex]x=\frac{6\times 3}{2}=9[/tex]
Hence, the line passing through the point (9,0) and (0,6) .Therefore, it represents the given graph.
Answer:c. [tex]y=-\frac{2}{3}x+6[/tex]
