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)?
y=(______)x+12

Answer 1

Explanation:

Explanation:

Step 1

Find the slope of the given line

we have

Isolate the variable y

The slope of the given line is

Step 2

Find the slope of the line that is parallel to the given line

we know that

if two lines are parallel, then their slopes are the same

so

----> slope of the given line

----> slope of the line parallel to the given line

Step 3

Find the equation of the line parallel to the given line that passes through the point

we know that

the equation of the line in slope-intercept form is equal to

where

m is the slope of the line

b is the y-intercept (value of y when the value of x is equal to zero)

In this problem we have

-------> this is the y-intercept

so

substitute

the equation of the line is

Answer 2

The equation of the line is
`y=-5x+12`

Explanation:

Step 1

Find the slope of the given line

we have

`10x+2y=-2`

Isolate the variable y

`2y=-10x-2`

`y=-5x-1`

The slope of the given line is

`m=-5`

Step 2

Find the slope of the line that is parallel to the given line

we know that

if two lines are parallel, then their slopes are the same

so

`m1=m2`

`m1=-5` ----> slope of the given line

`m2=-5` ----> slope of the line parallel to the given line

Step 3

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

we know that

the equation of the line in slope-intercept form is equal to

`y=mx+b`

where

m is the slope of the line

b is the y-intercept (value of y when the value of x is equal to zero)

In this problem we have

`m=-5`

`Point(0,12)` -------> this is the y-intercept

so

`b=12`

substitute

the equation of the line is

`y=-5x+12`