# How do you write an equation of a line going through (7,1) parallel to y=-x+3?

##### 1 Answer
Oct 10, 2016

$y = - x + 8$

#### Explanation:

Equations that are parallel have the same slope.

The standard equation of an equation is written through slope intercept form, which is $y = m x + b$ where m is your slope and b is the y intercept

So, in the equation provided, -1 is the slope.

To write an equation when given a slope and points, you use point slope form, which is $y - {y}_{1} = m \left(x - {x}_{1}\right)$

${y}_{1}$ is the y in the set of points you are given, same with ${x}_{1}$

So, ${y}_{1} = 1$ and ${x}_{2} = 7$

As stated before, m is the slope, and the slope is given as -1

Plug in the numbers into the equation

$y - 1 = - 1 \left(x - 7\right)$

Distribute -1 throughout the parenthesis

$y - 1 = - x + 7$

Add 1 on both sides of the equation

$y = - x + 8$

And there you have a equation parallel to $y = - x + 3$