A line passes through the points (–5, 2) and (10, –1). Which is the equation of the line?

1 answer:

7 0

$\bf (\stackrel{x_1}{-5}~,~\stackrel{y_1}{2})\qquad 
(\stackrel{x_2}{10}~,~\stackrel{y_2}{-1})
\\\\\\
% slope = m
slope = m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-2}{10-(-5)}\implies \cfrac{-1-2}{10+5}
\\\\\\
\cfrac{-3}{15}\implies \cfrac{-1}{5}
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-2=-\cfrac{1}{5}[x-(-5)]
\\\\\\
y-2=-\cfrac{1}{5}(x+5)\implies y-2=-\cfrac{1}{5}x-1\implies y=-\cfrac{1}{5}x+1$

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