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)?

$\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 0 &,& -3~) % (c,d) &&(~ 2 &,& 3~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{3-(-3)}{2-0}\implies \cfrac{3+3}{2-0}\implies 3$

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

$\bf \begin{array}{ccccccccc} &&x_1&&y_1\\ % (a,b) &&(~ -1 &,& -1~) \end{array} \\\\\\ % slope = m slope = m\implies 3 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-1)=3[x-(-1)] \\\\\\ y+1=3(x+1)$

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

$m=\frac{(y2-y1)}{(x2-x1)}$

substitute the values in the formula

$mAB=\frac{(3+3)}{(2-0)}$

$mAB=\frac{(6)}{(2)}$

$mAB=3$

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

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