Question

What is the equation of the line that is parallel to the given line and passes through the point (–2, 2)?

y = x + 4
y = x +
y = –5x + 4
y = –5x +

Answer 1

we know that

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

Step 1

Find the slope of the given line

we know that

the formula to calculate the slope between two points is equal to

`m=((y2-y1))/((x2-x1))`

in this problem we have

`(x1,y1)=(-5,-4)\\(x2,y2)=(0,-3)`

substitute in the formula

`m=((-3+4))/((0+5))`

`m=((1))/((5))`

`m=(1)/(5)`

Step 2

Find the equation of the line

we know that

the equation of the line into point-slope form is equal to

`y-y1=m(x-x1)`

we have

`m=(1)/(5)`

`(x1,y1)=(-2,2)`

substitute

`y-2=(1)/(5)(x+2)`

`y=(1)/(5)x+(2)/(5)+2`

`y=(1)/(5)x+(12)/(5)`

therefore

the answer is

`y=(1)/(5)x+(12)/(5)`