# What is the y-intercept of the line that is parallel to 2x + 3y = 4 and contains the point (6, -2)?

Mar 4, 2018

the given equation is,

$2 x + 3 y = 4$

or, $y = - \frac{2}{3} x + \frac{4}{3}$

now,let the equation of the line required be $y = m x + c$,where, $m$ is the slope and $c$ is the intercept.

Now,for both the lines to be parallel,slopes must be the same,so we get, $m = - \frac{2}{3}$

So,the equation of the line becomes, $y = - \frac{2}{3} x + c$

Now,given that the line passes through point $\left(6 , - 2\right)$,so putting in the equation we get,

$- 2 = \left(- \frac{2}{3}\right) \cdot 6 + c$

or, $c = 2$

And the equation becomes, $y = - \frac{2}{3} x + 2$ graph{y=-2/3x+2 [-10, 10, -5, 5]}