Answer
$m=\dfrac{15}{2}$
Work Step by Step
With the given points, $\left(
0, -\dfrac{1}{2}
\right)$ and $\left(
\dfrac{7}{5}, 10
\right)$, then
\begin{array}{l}\require{cancel}
y_1=
-\dfrac{1}{2}
,\\y_2=
10
,\\x_1=
0
,\text{ and }\\ x_2=
\dfrac{7}{5}
.\end{array}
Using $m=\dfrac{y_1-y_2}{x_1-x_2}$ or the Slope Formula, the slope, $m,$ of the line is
\begin{array}{l}\require{cancel}
m=\dfrac{-\dfrac{1}{2}-10}{0-\dfrac{7}{5}}
\\\\
m=\dfrac{-\dfrac{1}{2}-\dfrac{20}{2}}{0-\dfrac{7}{5}}
\\\\
m=\dfrac{-\dfrac{21}{2}}{-\dfrac{7}{5}}
\\\\
m=\dfrac{\dfrac{21}{2}}{\dfrac{7}{5}}
\\\\
m=\dfrac{21}{2}\div\dfrac{7}{5}
\\\\
m=\dfrac{21}{2}\cdot\dfrac{5}{7}
\\\\
m=\dfrac{\cancel{21}^3}{2}\cdot\dfrac{5}{\cancel7^1}
\\\\
m=\dfrac{3}{2}\cdot\dfrac{5}{1}
\\\\
m=\dfrac{15}{2}
.\end{array}
Hence, the slope is $
m=\dfrac{15}{2}
$.
