[tex]y-4=3(x+2)[/tex] equation describes the line in the graph.
What is point-slope form?
The point slope form is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point.
The point slope form of the line is [tex]y-y_{1} =k(x-x_{1})[/tex].
Given
[tex](x_{1},y_{1} )=(-2,4)[/tex]
[tex](x_{2},y_{2} )=(1,13)[/tex]
Slope(k) is [tex]\frac{x_{2}-x_{1} }{y_{2}-y_{1} }[/tex] = [tex]\frac{13-4}{1-(-2)}[/tex] = 3
The point-slope form of the line is [tex]y-y_{1} =k(x-x_{1})[/tex] ….(1)
k is the slope. k = 3
Substituting the values of k =3 and [tex](x_{1},y_{1} )=(-2,4)[/tex] in equation 1
⇒ [tex]y-4=3(x+2)[/tex]
Hence, [tex]y-4=3(x+2)[/tex] equation describes the line in the graph.
Option D is correct.
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