Question

What is an equation of the line that passes through the points (4, -6)
and (8, -4)

Answer 1

y = 1/2x - 8.

Explanation:

The slope of the line = rise / run

= (-4 - (-6)) / (8 - 4)

= 2/4

= 1/2.

Using the point/slope form of the equation of a line:

y - y1 = m(x - x1)

Here we have m = 1/2 and (x1, y1) = (4, -6):

y - (-6) = 1/2 (x - 4)

y + 6 = 1/2x - 2

y = 1/2x - 8.

Answer 2

`\bf (\stackrel{x_1}{4}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-4}-\stackrel{y1}{(-6)}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{4}}}\implies \cfrac{-4+6}{4}\implies \cfrac{2}{4}\implies \cfrac{1}{2}`

`\bf \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-\stackrel{y_1}{(-6)}=\stackrel{m}{\cfrac{1}{2}}(x-\stackrel{x_1}{4}) \\\\\\ y+6=\cfrac{1}{2}x-2\implies y=\cfrac{1}{2}x-8`