Answer: The equation is [y = -x +7]
Explanation: We are given a point and an equation (in <em>standard </em>form), and are told to find the equation of a line that is parallel to the equation given, and that contains the point given. Before we can even find the equation of the <em>unknown </em>line we must find, first change the equation we are <em>given </em>from <em>standard </em>form into <em>slope-intercept</em> form. In order to do this, subtract <em>x </em>from both sides of the <em>given </em>equation. This gives us the equation<em> y = -x - 1</em>.
Now that we have the <em>given </em>equation in <em>slope-intercept</em> form, we now know that the slope of the <em>given </em>equation is <em>-1</em>. The <em>unknown </em>equation contains a slope that is <em>parallel </em>to the slope of the <em>given </em>equation. This means that the slope of the <em>unknown</em> equation is <em>-1 as well</em>. Still with me so far? Good. It get's a little more complicated from here.
So, now that we have the slope of the <em>unknown</em> equation, this is where the given point comes in. This given point lies on the line of the <em>unknown </em>equation. This means that we can plug the slope of the <em>unknown </em>equation and the given point (which lies on the <em>unknown </em>equation) into point-slope form. Since the formula for the point-slope form is
, we plug in -1 for <em>m</em>(the slope), 2 for <em>y1</em>, and 5 for <em>x1</em>. This gives us the equation
. The <em>unknown </em>equation is now <em>known</em>. All that's left is to change this equation from point-slope form into slope-intercept form.
The first step is to distribute the slope. This changes our equation into
. The next step is to get <em>y</em> by itself. In order to do this, add <em>2 </em>to both sides of the equation. This gives us
, which is the answer.
Hope this helps! Have a great day!
<h3>
-Show work-</h3>
Given equation
![x+y=-1](https://tex.z-dn.net/?f=x%2By%3D-1)
![x-x+y=-x-1](https://tex.z-dn.net/?f=x-x%2By%3D-x-1)
![y = -x-1](https://tex.z-dn.net/?f=y%20%3D%20-x-1)
Unknown equation:
![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
![y-2=-1(x-5)](https://tex.z-dn.net/?f=y-2%3D-1%28x-5%29)
![y-2=-1(x) + -1(-5)](https://tex.z-dn.net/?f=y-2%3D-1%28x%29%20%2B%20-1%28-5%29)
![y-2=-x+5](https://tex.z-dn.net/?f=y-2%3D-x%2B5)
![y-2+2=-x+5+2](https://tex.z-dn.net/?f=y-2%2B2%3D-x%2B5%2B2)
![y=-x + 7](https://tex.z-dn.net/?f=y%3D-x%20%2B%207)