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)?
y + 1 = ( ? ) (x + 1)

Answer 1

well, parallel lines have the same exact slope, so hmmm what's the slope of the one that runs through (0, −3) and (2, 3)?




so, we're really looking for a line whose slope is 3, and runs through -1, -1

Answer 2

we know that

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

Step
`1`

Find the slope of the given line

Let

`A(0,-3)\\B(2,3)`

we know that

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

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

substitute the values in the formula

`mAB=((3+3))/((2-0))`

`mAB=((6))/((2))`

`mAB=3`

Step
`2`

Find the equation of the parallel line in the point slope form

we know that

`m=3\\Point (1,-1)`

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

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

substitute the values

`y+1=3*(x+1)`

therefore

the answer is

the equation in the point slope form is

`y+1=3*(x+1)`