Question

Write the equation of the line that passes through the points (8, –1) and (2, –5) in standard form, given that the point-slope form is y + 1 = 1/2 (x – 8).

Answer 1

The standard form is pretty much the variables on the left-hand-side and the constant alone by herself on the right-hand-side, with only positive integers on the x-variable and an integers all around.

$\bf y+1=\cfrac{1}{2}(x-8)\implies y+1=\cfrac{1}{2}x-4\implies y=\cfrac{1}{2}x-5 \\\\\\ -\cfrac{1}{2}x+y=-5\implies \stackrel{\textit{multiplying both sides by -1}}{\cfrac{1}{2}x-y=5} \\\\\\ \stackrel{\textit{and multiplying both sides by the LCD 2}}{x-2y=10}\impliedby standard~form$