Q. 2 - Precalculus Enhanced with Graphing Utilities

Question

(a) Graph the line : $3x+4y=12$.

(b) What is the slope of a line parallel to this line?

Step-by-Step Solution

Answer

(a) Graph of the line $3x+4y=12$ is shown below.

(b) The slope of the parallel line is $-\frac{3}{4}$ or $-0.75$.

Part (a) Step 1. Given information.

The given equation is:

$3x+4y=12$

Part (a) Step 2. Determine the intercepts.

Substitute $x=0$ to find y-intercept.

$\begin{array}{rcl}3\left(0\right)+4y& =& 12\\ 4y& =& 12\\ y& =& \frac{12}{4}\\ y& =& 3\end{array}$

Substitue $y=0$ to find the x-intercept.

$\begin{array}{rcl}3x+4\left(0\right)& =& 12\\ 3x& =& 12\\ x& =& \frac{12}{3}\\ x& =& 4\end{array}$

So, graph intersect the x-axis at $(4,0)$ and the y-axis at $(0,3).$

Part (a) Step 3. Draw the graph.

Plot the points $(0,3)$ and $(4,0)$ on a coordinate plane and connect them by a straight line.

Part (b) Step 1 Given information.

The given equation is:

$3x+4y=12$

Part (b) Step 2. Determine the slope of the parallel line.

The slope of the line $ax+by=c$ is $m=-\frac{a}{b}$.

In the given equation $a=3, b=4$. So, the slope of the given line is:

$m=-\frac{3}{4}$

The slopes of parallel lines are always equal. It means the slope of the parallel is $-\frac{3}{4}$ or $-0.75$.

Part (b) Step 3. Conclusion.

The slope of the parallel line is $-\frac{3}{4}$ or $-0.75$.