Question

What is the equation of a line that passing through points (-2, 5) and (3, 25)

Answer 1

$\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{25}) \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{25-5}{3-(-2)}\implies \cfrac{25-5}{3+2} \\\\\\ \cfrac{20}{5}\implies 4 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-5=4[x-(-2)] \\\\\\ y-5=4(x+2)\implies y-5=4x+8\implies y=4x+13$