Question

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

Answer 1

`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=mx+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(x-x_1)`

`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(x-7)`

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`