albamarronpe

2022-10-08

Write an equation of a line through (3,3) and parallel to y= 2/3x -1

Bleha7s

Beginner2022-10-09Added 11 answers

Our reference line is: $y=\frac{2}{3}x-1$

Hence the slope of the reference line is: $\frac{2}{3}$

Any straight line parallel to the reference line will have a slope of $\frac{2}{3}$

We are asked to find the equation of the line parallel to the reference line passing through the point (3,3).

The equation of a straight line passing through point (x1,y1) is:

$(y-{y}_{1})=m(x-{x}_{1})$ where m is the slope of the line.

Hence the equation of our required line will be:

$(y-3)=\frac{2}{3}(x-3)$

$3(y-3)=2(x-3)$

$3y-9=2x-6$

$3y=2x+3$

$y=\frac{2}{3}x+1$

Hence the slope of the reference line is: $\frac{2}{3}$

Any straight line parallel to the reference line will have a slope of $\frac{2}{3}$

We are asked to find the equation of the line parallel to the reference line passing through the point (3,3).

The equation of a straight line passing through point (x1,y1) is:

$(y-{y}_{1})=m(x-{x}_{1})$ where m is the slope of the line.

Hence the equation of our required line will be:

$(y-3)=\frac{2}{3}(x-3)$

$3(y-3)=2(x-3)$

$3y-9=2x-6$

$3y=2x+3$

$y=\frac{2}{3}x+1$

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