What is the equation for a line that passes through the points (-3,-3) and (6,21)?

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09-05-2018
Mathematics

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What is the equation for a line that passes through the points (-3,-3) and (6,21)?

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jdoe0001 jdoe0001 · Answer 1 · 2018-05-09T23:01:18+02:00

[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ -3 &,& -3~) % (c,d) &&(~ 6 &,& 21~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{21-(-3)}{6-(-3)}\implies \cfrac{21+3}{6+3}[/tex]

[tex]\bf \cfrac{24}{9}\implies \cfrac{8}{3} \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-3)=\cfrac{8}{3}[x-(-3)] \\\\\\ y+3=\cfrac{8}{3}(x+3)\implies y+3=\cfrac{8}{3}x+8\implies y=\cfrac{8}{3}x+5[/tex]