## Intermediate Algebra: Connecting Concepts through Application

Recall: The line $y=m x+b$ has a slope of $m$ and a $y$-intercept of $(0, b)$. Thus, the given line has $(0, -10)$ as $y$-intercept. Find the $x$-intercept by setting $y=0$ then solving for $x$ to obtain: \begin{align*} \require{cancel} y&=\frac{4}{5}x-10\\ 0&=\frac{4}{5}x-10\\ 10&=\frac{4}{5}x\\ \frac{5}{4} \cdot 10 &= \frac{4}{5}x \cdot \frac{5}{4}\\ \frac{5}{\cancel{4}^2} \cdot \cancel{10}^5 &= \cancel{\frac{4}{5}}x \cdot \cancel{\frac{5}{4}}\\ 12.5&=x \end{align*} Thus, the $x$-intercept is at $(12.5, 0)$. Plot the $x$ and $y$-intercepts; then connect them using a straight line. Refer to the graph above.