# How do you find an equation of the line having an x-intercept of 4 and parallel to 2x+Y=2?

May 14, 2016

$y = - 2 x + 8$

#### Explanation:

This question is asking us about slopes and intercepts. The x-intercept is given and the slope is hinted at by saying that the line we are looking for is parallel to another line. Parallel lines have the same slope.

We can start by finding the slope of the parallel line. Let's use the slope intercept form of the equation of a line to solve this, which is

$y = m x + b$

where $m$ is the slope and $b$ is the y-intercept. Casting our line $2 x + y = 2$ into this form we get

$y = - 2 x + 2$

from which we see that the slope, $m$, is $- 2$. Now we need to use the x-intercept information to find the equation of our line. The x-intercept occurs when $y = 0$, so we can substitute that into our equation along with the slope and solve for the remaining quantity, $b$

$0 = - 2 \left(4\right) + b$

which yields

$b = 8$

Therefore the equation of the line we are looking for is

$y = - 2 x + 8$