Question

Write the equation of the line that passes through the points (8,1) and (2,-5) in standard form, given the the point- slope for is y+1=2/3(x-8)

Answer 1

first off, those two points above do not give that point-slope form, however, the issue is just what's the standard form.

keeping in mind that standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

$\bf y+1=\cfrac{2}{3}(x-8)\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y+1)=3\left( \cfrac{2}{3}(x-8) \right)}\implies 3y+3=2(x-8) \\\\\\ 3y+3=2x-16\implies 3y=2x-19\implies -2x+3y=-19 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 2x-3y=19~\hfill$