Answer
$m=\dfrac{9}{4}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Convert the given equation, $
9x-4y=2
,$ to the Slope-Intercept Form to identify the slope of the line.
$\bf{\text{Solution Details:}}$
Using the properties of equality, in the Slope-Intercept Form which is given by $y=mx+b,$ the given equation is equivalent to
\begin{array}{l}\require{cancel}
9x-4y=2
\\\\
-4y=-9x+2
\\\\
y=\dfrac{-9x}{-4}+\dfrac{2}{-4}
\\\\
y=\dfrac{9}{4}x-\dfrac{1}{2}
.\end{array}
Since $m$ is the slope in the equation $y=mx+b,$ then the slope of the linear equation above is $
m=\dfrac{9}{4}
.$
