Answer:
Option 1 -
Step-by-step explanation:
Given : A given line has the equation ![10x+2y=-2](https://tex.z-dn.net/?f=10x%2B2y%3D-2)
To find : What is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0,
12)?
Solution :
The slope intercept form is
where, m is the slope and c is the y-intercept.
Writing given equation in slope intercept form,
Equation ![10x+2y=-2](https://tex.z-dn.net/?f=10x%2B2y%3D-2)
Take x to another side,
![2y=-10x-2](https://tex.z-dn.net/?f=2y%3D-10x-2)
Divide both side by 2,
![y=-5x-1](https://tex.z-dn.net/?f=y%3D-5x-1)
The slope intercept form of the equation is ![y=-5x-1](https://tex.z-dn.net/?f=y%3D-5x-1)
Where, m=-5 is the slope and c=-1 is the y-intercept.
When two lines are parallel their slopes are equal i.e. ![m_1=m_2](https://tex.z-dn.net/?f=m_1%3Dm_2)
Let the equation be ![y=mx+c](https://tex.z-dn.net/?f=y%3Dmx%2Bc)
As lines are parallel then m=-5
We have given lines passes through point (0,12).
Substitute in equation,
![12=-5(0)+c](https://tex.z-dn.net/?f=12%3D-5%280%29%2Bc)
![c=12](https://tex.z-dn.net/?f=c%3D12)
Substitute back in equation,
![y=-5x+12](https://tex.z-dn.net/?f=y%3D-5x%2B12)
Therefore, The required equation is ![y=-5x+12](https://tex.z-dn.net/?f=y%3D-5x%2B12)
So, Option 1 is correct.