Question

11.) Write the equation of the line that passes through the given point P and its PARALLEL to the line with the givenequation. P(-1,2), y = 2/3x - 2

Answer 1

ANSWER

$y=\frac{2}{3}x+\frac{8}{3}$

EXPLANATION

When a line is parallel to another line, they have equal slopes.

This means that the slope of the line is:

$m=\frac{2}{3}$

To find the equation of the line, apply the point-slope method:

$y-y_1=m(x-x_1)$

where (x1, y1) is the point the line passes through.

Therefore, we have:

$\begin{gathered} y-2=\frac{2}{3}(x-(-1)) \\ y-2=\frac{2}{3}(x+1) \\ y-2=\frac{2}{3}x+\frac{2}{3} \\ y=\frac{2}{3}x+\frac{2}{3}+2 \\ y=\frac{2}{3}x+\frac{8}{3} \end{gathered}$

That is the equation of the line.