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Write the equation in point-slope form theough (18,-2) and parallel to y = 5/9x +9

1 Answer

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The given equation is


y=(5)/(9)x+9

The slope of the given equation is 5/9. Remember that the slope is the coefficient of x.

Given that the new line must be parallel to the given equation, then the new line has a slope of 5/9 too.

Then, we use the point (18,-2), the slope, and the point-slope formula.


\begin{gathered} y-y_1=m(x-x_1) \\ y-(-2)=(5)/(9)(x-18) \\ y+2=(5)/(9)x-10 \\ y=(5)/(9)x-10-2 \\ y=(5)/(9)x-12 \end{gathered}

Therefore, the equation of the new parallel line is


y=(5)/(9)x-12

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