Question

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

Answer 1

y = negative one-fifth x + 1

Explanation:

Y=-1/5x + 1

Answer 2

`\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`