Question

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

Answer 1

Answer:

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

Step-by-step 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

$y=-5x+12$

Answer 2

Answer:

Step-by-step explanation:

Step-by-step 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