Chapter 9, Problem 5QC

To determine

Use a table of values to graph each equation.

Answer to Problem 5QC

The domain is all real numbers. The range is all real numbers.

Explanation of Solution

Given:

The equation: $4x-3y=12$

Concept Used:

A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is sometimes called a straight line or, more archaically, a right line, to emphasize that it has no "wiggles" anywhere along its length.

The domain of a function is the complete set of possible values of the independent variable. The domain is the set of all possible x-values which will make the function "work", and will output real y-values. 

The range of a function is the complete set of all possible resulting values of the dependent variable ( y,  usually), after we have substituted the domain.

Calculation:

Rewrite the equation in slope and intercept form:

  $\begin{array}{l}4x-3y=12\\ 4x-3y+3y=12+3y[\text{add}\text{3y}\text{to}\text{both}\text{sides}]\\ 4x=12+3y\\ 4x-12=12-12+3y[s\text{ubtract}\text{12}\text{from}\text{both}\text{sides}]\\ 4x-12=3y\\ \frac{4x-12}{3}=\frac{3y}{3}[\text{divide}\text{each}\text{side}\text{by}\text{3}]\\ y=\frac{4}{3}x-4\end{array}$

The equation: $y=\frac{4}{3}x-4$

Make table to get some points on the graph

x	$y=\frac{4}{3}x-4$	(x, y)
0	$y=\frac{4}{3}·0-4=-4$	(0, − 4)
− 3	$y=\frac{4}{3}·-3-4=-4-4=-8$	( − 3 ,− 8 )
−6	$y=\frac{4}{3}·-6-4=-8-4=-12$	(− 6 , − 12 )
3	$y=\frac{4}{3}·3-4=4-4=0$	(3, 0)
6	$y=\frac{4}{3}·6-4=8-4=4$	(6, 4)

Graph the ordered pairs, and connect them to create a smooth straight line. The straight line is having x and y intercept at x = 3 and y = − 4. Extended both sides to infinity

Slope − intercept form of a straight line is y = mx + b Where m is the slope of the line and b is the y − intercept. The graph is a straight line with a slope $\frac{4}{3}$ The domain is all real numbers. The range is all real numbers.