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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 4: Q. 95 (page 452)

In the following exercises, graph by plotting points.
$2 x + 3 y = 12$

Short Answer

Expert verified

The graph of the equation is

Step by step solution

01

Step 1. Given Information

In the given exercises we have to graph by plotting points.

$2 x + 3 y = 12$

02

Step 2. Find three points that are solutions to the equation.First, let x=0

$2 x + 3 y = 12 2 脳 0 + 3 y = 12$

Solve fory.

$3 y = 12 \frac{3}{3} y = \frac{12}{3} y = 4$

03

Step 3. Now let y=0

$2 x + 3 y = 12 2 x + 3 脳 0 = 12$

Solve for x.

$2 x = 12 \frac{2}{2} x = \frac{12}{2} x = 6$

04

Step 4. We need a third point. Remember, we can choose any value for x or y.We'll let x=3

$2 x + 3 y = 12 2 脳 3 + 3 y = 12 6 + 3 y = 12$

Subtract 6 on both side

$6 + 3 y - 6 = 12 - 6 3 y = 6$

Solve for y.

$\frac{3}{3} y = \frac{6}{3} y = 2$

05

Step 5. Plot all points in a rectangular coordinate system.Plot the points (0,4) (6,0), (3,2)

06

Step 6. Draw the lines through the three points.

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鈸� $(鈭� 2, 鈭� 3)$ 鈸� $(3, 鈭� 3)$ 鈸� $(鈭� 4, 1)$ 鈸� $(4, 鈭� 1)$ 鈸� $(\frac{3}{2}, 1)$

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