MATH SOLVE

4 months ago

Q:
# A line contains the points (-3, 4) and (7, -1). Calculate the equation of the line in the form y = mx + b Explain each step.

Accepted Solution

A:

[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-4}{7-(-3)}\implies \cfrac{-5}{7+3}\implies \cfrac{-5}{10}\implies -\cfrac{1}{2}[/tex][tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-4=-\cfrac{1}{2}[x-(-3)]\implies y-4=-\cfrac{1}{2}(x+3) \\\\\\ y-4=-\cfrac{1}{2}x-\cfrac{3}{2}\implies y=-\cfrac{1}{2}x-\cfrac{3}{2}+4\implies y=-\cfrac{1}{2}x+\cfrac{5}{2}[/tex]