MATH SOLVE

4 months ago

Q:
# 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)

Accepted Solution

A:

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)?

[tex]\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[/tex]

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

[tex]\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)[/tex]

[tex]\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[/tex]

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

[tex]\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)[/tex]