Answer
The slope of the line is $m=\frac{a}{b}$.The line rises from left to right.
Work Step by Step
Consider a line passing through the points $\left( a-b,c \right)$ and $\left( a,a+c \right)$.
For a line passing through two different points $\left( {{x}_{1}},{{y}_{1}} \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)$, the slope is given by the following equation:
$m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$
Substitute $\left( {{x}_{1}},{{y}_{1}} \right)=\left( a-b,c \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)=\left( a,a+c \right)$, and find the slope as below:
$\begin{align}
& m=\frac{\left( a+c \right)-c}{a-\left( a-b \right)} \\
& =\frac{a+c-c}{a-a+b} \\
& =\frac{a}{b}
\end{align}$
Where a and b are positive real numbers. So, the quantity $\frac{a}{b}$ will be positive. Thus, the slope of the given line will be positive.
Positive slope indicates that the line will rise from left to right.
