Chapter 9, Problem 6QC

To determine

Use a table of values to graph each equation.

Answer to Problem 6QC

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

Explanation of Solution

Given:

The equation: $3y=6+9x$

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:

  $\begin{array}{l}3y=6+9x\\ \frac{3y}{3}=\frac{9x+6}{3}[\text{divide}\text{each}\text{side}\text{by}\text{3}]\\ y=3x+2\end{array}$

The equation: $y=3x+2$

Make table to get some points on the graph

x	$y=3x+2$	(x, y)
0	$y=3·0+2=2$	(0, 2)
− 1	$y=3·-1+2=-3+2=-1$	( − 1 ,− 1 )
− 2	$y=3·-2+2=-6+2=-4$	(− 2 , − 4 )
1	$y=3·1+2=3+2=5$	(1, 5)
2	$y=3·2+2=6+2=8$	(2, 8)

Graph the ordered pairs, and connect them to create a smooth straight line. The straight line is having x and y intercept at x = $-\frac{2}{3}$ and y = − 2. 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 3 The domain is all real numbers. The range is all real numbers.

Thus, the domain is all real numbers. The range is all real numbers.