Answer:
C. y+2=−3(x−1)
Step-by-step explanation:
To know what is the equation graphed in the figure you should give values to x on the interval (-1,2) and solve for y.
Finally you should compare the obtained values with the graph. Note that you have the following points on the graph: (-1,4); (0,1); (1,2); (2,-5).
1. When x=-1
[tex]A. y-4=-13(x+2)\\\\y-4=-13(-1+2)\\\\y-4=-13(1)\\\\y-4=-13\\\\y=-13+4\\\\y=-9[/tex]
(-1,9)
[tex]B. y-3=13(x+1)\\\\y-3=13(-1+1)\\\\y-3=13(0)\\\\y-3=0\\\\y=3[/tex]
(-1,3)
[tex]C. y+2=-3(x-1)\\\\y+2=-3(-1-1)\\\\y+2=-3(-2)\\\\y+2=6\\\\y=6-2\\\\y=4[/tex]
(-1,4)
[tex]D. y-5=3(-1-1)\\\\y-5=3(-2)\\\\y-5=-6\\\\y=-6+5\\\\y=-1[/tex]
(-1,-1)
2. When x=0
[tex]A. y-4=-13(x+2)\\\\y-4=-13(0+2)\\\\y-4=-13(2)\\\\y-4=-26\\\\y=-26+4\\\\y=-22[/tex]
(0,22)
[tex]B. y-3=13(x+1)\\\\y-3=13(0+1)\\\\y-3=13(1)\\\\y-3=13\\\\y=13+3\\\\y=16[/tex]
(0,16)
[tex]C. y+2=-3(x-1)\\\\y+2=-3(0-1)\\\\y+2=-3(-1)\\\\y+2=3\\\\y=3-2\\\\y=1[/tex]
(0,1)
[tex]D. y-5=3(x-1)\\\\y-5=3(0-1)\\\\y-5=3(-1)\\\\y-5=-3\\\\y=-3+5\\\\y=2[/tex]
(0,2)
The equation C. y+2=−3(x−1) give the solution points (-1,4), and (0,1), therefore this equation is graphed in the figure.
