Question

E. Line e goes through the point (8,-1) and has a

slope of -3/4.
Equation or Explanation:

Answer 1

`y_e = -\frac34x + 5`

Explanation:

The equation of a line, if given its slope and one point that it passes through, is given by the formula
`y - y_1 = m(x - x_1)`.

Therefore, we can substitute
`m = -\frac34`,
`x_1 = 8` and
`y_1 = -1` into the formula above.

`y - (-1) = -\frac34(x - 8)\\\\\to y + 1 = -\frac34x + 6\\\\\to y = -\frac34x + 5`

Answer 2

`(\stackrel{x_1}{8}~,~\stackrel{y_1}{-1})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{3}{4} \\\\\\ \begin{array}c \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{- \cfrac{3}{4}}(x-\stackrel{x_1}{8}) \implies y +1= -\cfrac{3}{4} (x -8) \\\\\\ y+1=-\cfrac{3}{4}x+6\implies {\LARGE \begin{array}{llll} y=-\cfrac{3}{4}x+5 \end{array}}`