Question

The given line passes through the points (0,-3) and (2,3). What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (-1,-1)?

Answer 1

y+1=3(x+1)

Explanation:

slope= (3-(-3))/(2-0) = 3

y=3x+b

-1=3(-1)+b

b=-2

y=3x-2

Convert to point slope form:

y+1=3(x+1)

Answer 2

`y=3x+2`

Explanation:

Given : The given line passes through the points (0,-3) and (2,3).

To Find: What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (-1,-1)?

Solution:

Points : (0,-3) and (2,3).

To find the equation of given points we will use two point slope form

Formula :
`y-y_1=m(x-x_1)` --A

Where m is the slope

`m = (y_2-y_1)/(x_2-x_1)`

`(x_1,y_1)=(0,-3)`

`(x_2,y_2)=(2,3)`

So,
`m = (3-(-3))/(2-0)`

`m = (6)/(2)`

`m = 3`

Now substitute the values in A

`y+3=3(x-0)`

`y+3=3x`

Two lines are said to be parallel when they have same slope

So, The line parallel to the given line will have slope =3

General form of equation of line =
`y=mx+c`

Substitute m = 3

So, parallel line :
`y=3x+c` ---B

Now this parallel lines passes through point (-1,-1)

So, substitute this point in B

`-1=3(-1)+c`

`-1=-3+c`

`2=c`

Substitute value of c in B

So, Equation of parallel line =
`y=3x+2`

Hence the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (-1,-1) is
`y=3x+2`