# How do you write an equation of a line through (3,3) and parallel to y= 2/3x -1?

Apr 4, 2017

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

#### Explanation:

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 $\left(3 , 3\right)$.

The equation of a straight line passing through point $\left({x}_{1} , {y}_{1}\right)$ is:

$\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$ Where $m$ is the slope of the line.

Hence the equation of our required line will be:

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

$3 \left(y - 3\right) = 2 \left(x - 3\right)$

$3 y - 9 = 2 x - 6$

$3 y = 2 x + 3$

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