Beginning Algebra With Applications, Chapter 5, 5.3, Section 5.3, Problem 60

Suppose $A, B$ and $C$ are all positive numbers. Does the $y$-intercept of the graph of $Ax + By = C$ lie above or below the $x$-axis? Does the graph slant upward to the right or downward to the right?

If we rewrite the equation in slope intercept form, we get


$
\begin{equation}
\begin{aligned}

Ax + By =& C
\\
\\
By =& C - Ax
\\
\\
y =& \frac{C - Ax}{B}
\\
\\
y =& \frac{-A}{B}x + \frac{C}{B}

\end{aligned}
\end{equation}
$


The value of $\displaystyle \frac{C}{B}$ the $y$-intercept, since $B$ and $C$ are both positive numbers. Then the $y$-intercept must be a positive number and does lies above the $x$-axis. Next, the value of $\displaystyle \frac{-A}{B}$ determines the slope of the line, it also determines if the line slant upward to the right or downward to the right. Since $A$ is a negative number and $B$ is a positive number then the slope must be positive making the graph slant upward to the right.