# How do you find the equation of the line which has a y-intercept of 13 and is parallel to the line joining the points (8, 12) and (-9, 10)?

Jun 28, 2016

$2 x - 17 y = - 221$

#### Explanation:

A line with a y-intercept of 13 passes through the point $\left(0 , 13\right)$ (by definition of y-intercept)

A line parallel to the line joining the points $\left(8 , 12\right)$ and $\left(- 9 , 10\right)$
has the same slope as the line joining $\left(8 , 12\right)$ and $\left(- 9 , 10\right)$, namely
$\textcolor{w h i t e}{\text{XXX}} m = \frac{\Delta y}{\Delta x} = \frac{12 - 10}{8 - \left(- 9\right)} = \frac{2}{17}$

Using the point-slope form:
$\textcolor{w h i t e}{\text{XXX}} y - 13 = \frac{2}{17} \left(x - 0\right)$

$\textcolor{w h i t e}{\text{XXX}} 17 y - 17 \times 13 = 2 x$

$\textcolor{w h i t e}{\text{XXX}} 2 x - 17 y = - 221$

graph{(2x-17y+221)((x-8)^2+(y-12)^2-0.1)((x+9)^2+(y-10)^2-0.1)=0 [-14.63, 17.4, 5.02, 21.04]}