Question

A given line has the equation 10x+2y=-2.

Answer 1

Answer:

Option 1 - $y=-5x+12$                              

Step-by-step explanation:

Given : A given line has the equation $10x+2y=-2$

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 $y=mx+c$

where, m is the slope and c is the y-intercept.

Writing given equation in slope intercept form,

Equation $10x+2y=-2$

Take x to another side,

$2y=-10x-2$

Divide both side by 2,

$y=-5x-1$

The slope intercept form of the equation is $y=-5x-1$

Where, m=-5 is the slope and c=-1 is the y-intercept.

When two lines are parallel their slopes are equal i.e. $m_1=m_2$

Let the equation be $y=mx+c$

As lines are parallel then m=-5

We have given lines passes through point (0,12).

Substitute in equation,

$12=-5(0)+c$

$c=12$

Substitute back in equation,

$y=-5x+12$

Therefore, The required equation is $y=-5x+12$

So, Option 1 is correct.

Answer 2

Answer:

5x+y=12

Step-by-step explanation:

10x+2y=-2=5x+y=12