Answer:
![y=2x+3](https://tex.z-dn.net/?f=y%3D2x%2B3)
Step-by-step explanation:
The slope-intercept form is
, where
is the slope and
is the y-intercept.
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
Using the slope-intercept form, the slope is 2.
![m=2](https://tex.z-dn.net/?f=m%3D2)
So in order for us to find an equation that is parallel, the slopes must be equal. We need to find the parallel line using the point-slope formula.
We use the slope 2 and a given point
to substitute for x1 and y1 in the point-slope form
, which is derived from the slope equation: ![m=\frac{y2-y1}{x2-x1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By2-y1%7D%7Bx2-x1%7D)
Now we simplify the equation and keep it in point-slope form.
× ![(x-2)](https://tex.z-dn.net/?f=%28x-2%29)
Simplify
× ![(x-2)](https://tex.z-dn.net/?f=%28x-2%29)
![y-7=2x-4](https://tex.z-dn.net/?f=y-7%3D2x-4)
![Rewrite.~y-7=0+0+2~x~(x-2)](https://tex.z-dn.net/?f=Rewrite.~y-7%3D0%2B0%2B2~x~%28x-2%29)
![Simplify~ by~adding~zeros.~y-7=2 ~x~(x-2)](https://tex.z-dn.net/?f=Simplify~%20by~adding~zeros.~y-7%3D2%20~x~%28x-2%29)
![Apply~the~distributive~property.~y-7=2x+2~X~-2](https://tex.z-dn.net/?f=Apply~the~distributive~property.~y-7%3D2x%2B2~X~-2)
![Multiply~2~by~-2.~y-7=2x-4](https://tex.z-dn.net/?f=Multiply~2~by~-2.~y-7%3D2x-4)
Last, We move all terms not containing y to the right side of the equation.
Add 7 to both sides of the equation.
![y=2x-4+7](https://tex.z-dn.net/?f=y%3D2x-4%2B7)
Add −4 and 7 and your answer will be: ![y=2x+3](https://tex.z-dn.net/?f=y%3D2x%2B3)