   Chapter 10.CT, Problem 6CT Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Using the table from Exercise 5, sketch the graph of 2 x + 3 y = 12 . To determine

To draw:

The graph of the equation 2x+3y=12

Explanation

To draw a graph for a equation,

First we need to find the x-intercept and y-intercept.

For finding the x-intercept, make y as 0 and solve for x in the given equation.

For finding the y-intercept, make x as 0 and solve for y in the given equation.

Substitute x=0 in the given equation 2x+3y=12,

20+3y=12

On simplifying,

3y=12

The coefficient of y is 3, thus divide both sides by 3.

3y3=123

y=4

Thus the first point is 0, 4.

Substitute x=3 in the given equation 2x+3y=12,

23+3y=12

On simplifying,

6+3y=12

3y=12-6

3y=6

The coefficient of y is 3, thus divide both sides by 3.

3y3=63

y=2

Thus the second point is 3, 2.

Substitute y=4 in the given equation 2x+3y=12,

2x+34=12

On simplifying,

2x+12=12

2x=12-12

2x=0

x=0

Thus the third point is 0, 4.

Substitute x=9 in the given equation 2x+3y=12,

29+3y=12

On simplifying,

18+3y=12

3y=12-18

3y=-6

The coefficient of y is 3, thus divide both sides by 3

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