Answer:
Option 1 - [tex]y=-5x+12[/tex]
Step-by-step explanation:
Given : A given line has the equation [tex]10x+2y=-2[/tex]
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 [tex]y=mx+c[/tex]
where, m is the slope and c is the y-intercept.
Writing given equation in slope intercept form,
Equation [tex]10x+2y=-2[/tex]
Take x to another side,
[tex]2y=-10x-2[/tex]
Divide both side by 2,
[tex]y=-5x-1[/tex]
The slope intercept form of the equation is [tex]y=-5x-1[/tex]
Where, m=-5 is the slope and c=-1 is the y-intercept.
When two lines are parallel their slopes are equal i.e. [tex]m_1=m_2[/tex]
Let the equation be [tex]y=mx+c[/tex]
As lines are parallel then m=-5
We have given lines passes through point (0,12).
Substitute in equation,
[tex]12=-5(0)+c[/tex]
[tex]c=12[/tex]
Substitute back in equation,
[tex]y=-5x+12[/tex]
Therefore, The required equation is [tex]y=-5x+12[/tex]
So, Option 1 is correct.
