The equation of line which passes through a given point and has a given slope is required.
The required equation is [tex]y=-\dfrac{2}{3}x-\dfrac{19}{3}[/tex]
The point the line passes though is [tex](1,-7)[/tex]
[tex]x_1=1[/tex]
[tex]y_1=-7[/tex]
m = Slope of the line = [tex]-\dfrac{2}{3}[/tex]
Point slope form is given by
[tex]y-y_1=m(x-x_1)[/tex]
Substituting the given values
[tex]y-(-7)=-\dfrac{2}{3}(x-1)\\\Rightarrow y+7=-\dfrac{2}{3}x+\dfrac{2}{3}\\\Rightarrow y=-\dfrac{2}{3}x+\dfrac{2}{3}-7\\\Rightarrow y=-\dfrac{2}{3}x-\dfrac{19}{3}[/tex]
The required equation is [tex]y=-\dfrac{2}{3}x-\dfrac{19}{3}[/tex]
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