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