# How do you write an equation of a line going through (4,1) parallel to y=1/3x+3?

May 5, 2018

$x - 3 y - 1 = 0$

#### Explanation:

When a line is parallel to another line, that means that their gradients are the same ie your new line will have the gradient $m = \frac{1}{3}$ since $y = \frac{1}{3} x + 3$ is in the general form $y = m x + b$ where m is the gradient

$\left(y - 1\right) = \frac{1}{3} \left(x - 4\right)$
$3 y - 3 = x - 4$
$x - 3 y - 1 = 0$