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Chapter 2: Q. 11 (page 126)

Graph the equation:
$3 x - 2 y = 12$

Short Answer

Expert verified

The graph of the given equation is:

Step by step solution

01

Step 1. Given Information

The given equation is $3 x - 2 y = 12$

02

Step 2. Make a table for values

Writing the equation in terms of $y$ , we get:

$3 x - 2 y = 12 2 y = 3 x - 12 y = \frac{3}{2} x - 6$

Table of values for $x$ and $y$ is:

$x$	$y = \frac{3}{2} x - 6$
$0$	$y = \frac{3}{2} \times 0 - 6 y = - 6$
$1$	role="math" localid="1645949411197" $y = \frac{3}{2} \times 1 - 6 y = \frac{3}{2} - 6 y = \frac{- 9}{2}$
$2$	$y = \frac{3}{2} \times 2 - 6 y = 3 - 6 y = - 3$
$3$	$y = \frac{3}{2} \times 3 - 6 y = \frac{9}{2} - 6 y = \frac{- 3}{2}$

03

Step 3. Graph the function

Plotting these points on the same cartesian plane and joining them to find them, we get:

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Most popular questions from this chapter

The short-term

(no more than $24$ hours) parking fee F (in dollars) for

parking x hours at O’Hare International Airport’s main

parking garage can be modeled by the function

role="math" localid="1645828501222" $F (x) = \{\begin{cases} 2 & i f 0 < x \leq 1 \\ 4 & i f 1 < x \leq 3 \\ 10 & i f 3 < x \leq 4 \\ 5 i n t (x + 1) + 2 & i f 4 < x < 9 \\ 51 & i f 9 \leq x \leq 24 \end{cases}$

Determine the fee for parking in the short-term parking

garage for

(a) $2$ hours

(b) $7$ hours

(c) $15$ hours

(d) $8$ hours and $24$ minutes

True or False The cube function is odd and is increasing on the interval $(- \infty, \infty)$ .

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

$f (x) = x^{2} + 4$

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

$g (x) = \frac{1}{2} \sqrt{x}$

Suppose that the graph of a function $g$ is known. The graph of $y = g (x) + 2$ may be obtained by a _______ shift of the graph of $g$ ________ a distance of $2$ units.

See all solutions

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