Question

The point-slope form of the equation of the line that passes through (–4, –3) and (12, 1) is y – 1 = (x – 12). What is the standard form of the equation for this line?

Answer 1

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

so, let's multiply both sides by the LCD of all fractions, in this case that'd be 4, to do away with the denominators.

`\bf y-1=\cfrac{1}{4}(x-12)\implies \stackrel{\textit{multiplying by }\stackrel{LCD}{4}}{4y-4=x-12}\implies 4y=x-8 \\\\\\ -x+4y=-8\implies \boxed{x-4y=8}`