Question

Find the equation of the line that goes through the points (4, –1) and (2, –5).

Use slope formula,equation,to find the slope of a line that passes through the points.

m =
Use slope-intercept form, y = mx + b, to find the y-intercept (b) of the line.

b =
Write the equation in slope-intercept form, y = mx + b.

Answer 1

`\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-5}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-5-(-1)}{2-4}\implies \cfrac{-5+1}{-2}\implies \cfrac{-4}{-2}\implies 2 \\\\\\ \begin{array}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-(-1)=2(x-4) \\\\\\ y+1=2x-8\implies y=2x-9`

Answer 2

m= 2

b= -9

equation= y=2x-9

Explanation: