Question

Write an equation in standard form of a line with m= 6/7 and b = -2

Answer 1

`\bf \begin{array}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}~\hspace{10em}y=\stackrel{\downarrow }{\cfrac{6}{7}}x\underset{\uparrow }{-2}`

now, let's bear 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, that way we do away with the denominators.

`\bf \stackrel{\textit{multiplying by }\stackrel{LCD}{7}}{7(y)=7\left( \cfrac{6x}{7}-2 \right)}\implies 7y=6x-14 \\\\\\ -6x+7y=-14\implies \blacktriangleright 6x-7y=14 \blacktriangleleft`