How do you graph the line that passes through (2,-1) parallel to the line 2x+3y=6?

May 5, 2018

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

Explanation:

1. First, we manipulate the given equation into $y = m x + c$ to find the gradient.
$2 x + 3 y = 6$
$3 y = - 2 x + 6$
$y = - \frac{2}{3} x + 2$
$\therefore G r a \mathrm{di} e n t = - \frac{2}{3}$

Since the lines are parallel, they have the same gradient.

1. Form an equation for the line.
Let the equation of the line be $y - {y}_{1} = m \left(x - {x}_{1}\right)$.
$y - \left(- 1\right) = - \frac{2}{3} \left(x - 2\right)$
$y = - \frac{2}{3} x + \frac{1}{3}$