Question

Which equation represents a line with slope 2/3 and y-intercept –6?

Answer 1

Answer:

The answer would be

D. 2x − 3y = 18

Step-by-step explanation:

Answer 2

$\bf \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \implies \qquad y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{2}{3}}x\stackrel{\stackrel{b}{\downarrow }}{-6}$

bearing 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

$\bf \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y)=3\left( \cfrac{2}{3}x-6 \right)}\implies 3y=2x-18 \\\\\\ -2x+3y=-18\implies 2x-3y=18$