Answer:
c. \(y=-\frac{2}{3}x+6\)
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.\(y=-2x-6\)
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. \(y=\frac{2}{3}x+6\)
Substitute y=0 then, we get
\(\frac{2}{3}x+6=0\)
\(\frac{2}{3}x=-6\)
\(x=\frac{-6\times 3}{2}=-9\)
The x- intercept =-9
But , we have x=9
Therefore, it is false.
c. \(y=-\frac{2}{3}x+6\)
Substitute x=0 then we get
y=6
Substitute y=0
Then, we get
\(-\frac{2}{3}x+6=0\)
\(\frac{2}{3}x=6\)
\(x=\frac{6\times 3}{2}=9\)
Hence, the line passing through the point (9,0) and (0,6) .Therefore, it represents the given graph.
Answer:c. \(y=-\frac{2}{3}x+6\)
