Answer
slope = $\dfrac{a}{b}$;
The line through the two given points rises from left to right.
Work Step by Step
RECALL:
(i) The slope, $m$, of the line that passes through the points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula:
$m=\dfrac{y_2-y_1}{x_2-x_1}$
(ii) A line whose slope is positive rises from left to right.
(iii) A line whose slope is negative falls from left to right.
(iv) A horizontal line has a slope of zero.
(v) A vertical line has an undefined slope.
Use the formula in (i) above to find the slope of the line that passes through the points $(a-b, c)$ and $(a, a+c)$ to obtain:
$m=\dfrac{(a+c) -c }{a-(a-b)}
\\m=\dfrac{a+c-c}{a-a+b}
\\m=\dfrac{a}{b}$
$\dfrac{a}{b}$ is positive.
Thus, the line through the two given points rises from left to right.
