Question

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

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)?

Answer 1

y = -5x + 12 since the slope of that line is -5x and in order to pass through that point the y intercept must be 12

Answer 2

Step 1

Find the slope of the given line

we have

`10x+2y=-2`

Isolate the variable y

Subtract
`10x` both sides

`2y=-10x-2`

Divide by
`2` both sides

`y=-5x-1`

The slope of the given line is

`m=-5`

Step 2

Find the equation of the line that is parallel to the given line and passes through the point
`(0, 12)`

we know that

If two lines are parallel. then their slope are equal

In this problem we have

`m=-5`

`(0, 12)`

The equation of the line into slope-intercept form is equal to

`y=mx+b`

substitute the values

`12=-5*0+b`

`b=12`

the equation of the line is

`y=-5x+12`

therefore

the answer is

`y=-5x+12`