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2 years ago

14

I am trying to find the equation of the following lines, i’m just having trouble putting them in slope-intercept form.

1 answer:

Margaret [11]2 years ago

7 0

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1\\
&&(~ -1 &,& -6~)
\end{array}
\\\\\\
slope = m\implies \cfrac{2}{5}
\\\\\\
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-6)=\cfrac{2}{5}[x-(-1)]
\\\\\\
y+6=\cfrac{2}{5}(x+1)\implies y+6=\cfrac{2}{5}x+\cfrac{2}{5}
\\\\\\
y=\cfrac{2}{5}x+\cfrac{2}{5}-6\implies y=\cfrac{2}{5}x-\cfrac{28}{5}$

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
&&(~ -2 &,& 5~) 
&&(~ 5 &,& 8~)
\end{array}
\\\\\\
slope = m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{8-5}{5-(-2)}\implies \cfrac{8-5}{5+2}\implies \cfrac{3}{7}
\\\\\\
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-5=\cfrac{3}{7}[x-(-2)]
\\\\\\
y-5=\cfrac{3}{7}(x+2)\implies y-5=\cfrac{3}{7}x+\cfrac{6}{7}
\\\\\\
y=\cfrac{3}{7}x+\cfrac{6}{7}+5\implies y=\cfrac{3}{7}x+\cfrac{41}{7}$

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