Question

A line with a slope of -1 passes through the point (2,-1). If (-4, p) is another point on the line,

what is the value of p?

Answer 1

`(\stackrel{x_1}{2}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{p}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{p}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{2}}}~~= ~~\stackrel{\stackrel{m}{\downarrow }}{-1}\implies \cfrac{p+1}{-6}=-1\implies p+1=6\implies p=5`