Question

Find the point slope equation for the line that passes through the points (7,-21) (-4,23)

Answer 1

See Below

Explanation:

The point slope equation follows − ^1 = ( − ^1).

To find m, follow the formula
`(y2 - y1)/(x2 -x1)`

In this case,
`m = (23-(-21))/(-4-7) = -4`

Hence, the point-slope equation is
`y + 21 = -4 (x - 7)`, or alternatively,

`y - 23 = -4 (x+4)`

Answer 2

`\bf (\stackrel{x_1}{7}~,~\stackrel{y_1}{-21})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{23}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{23-(-21)}{-4-7}\implies \cfrac{23+21}{-11}\\\\\\ \cfrac{44}{-11}\implies -4 \\\\\\ \begin{array} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-21)=-4(x-7)\implies y+21=-4(x-7)`