# How do you write an equation of a line through (5,-1) parallel to y=1/9x+1?

Nov 15, 2016

$y + 1 = \frac{1}{9} \left(x - 5\right)$
$y = \frac{1}{9} x - \frac{14}{9}$

#### Explanation:

From the given line, we know that the slope of the new line must be the same as the slope of the old line because they are parallel.

• Slope is $\frac{1}{9}$
• Point is at $\left(5 , - 1\right)$ (given point that new line passes through)

Point-slope form:
$y + 1 = \frac{1}{9} \left(x - 5\right)$

Slope intercept form:
$y = \frac{1}{9} \left(x - 5\right) - 1$
$y = \frac{1}{9} x - \frac{5}{9} - 1$

$y = \frac{1}{9} x - \frac{14}{9}$