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

Answer:

y+1=3(x+1)

Step-by-step 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

Answer:

$y=3x+2$

Step-by-step 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

$m = \frac{y_2-y_1}{x_2-x_1}$

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

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

So, $m = \frac{3-(-3)}{2-0}$

$m = \frac{6}{2}$

$m = 3$

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  $y=3x+2$