Download presentation

1
**4.5 Graphing Linear Equations**

A linear equation can be written in the form Ax + By = C. This is called the standard form of a linear equation. A ≥ 0, A and B are not both zero, and A, B, and C are integers whose greatest common factor is 1.

2
**Identify Linear Equations**

Determine whether each equation is a linear equation. If so, write the equation in standard form. y = 5 – 2x y + 2x = 5 – 2x + 2x 2x + y = 5 The equation is now in standard form where A = 2, B = 1, and C = 5. This is a linear equation.

3
**Identify Linear Equations**

Determine whether each equation is a linear equation. If so, write the equation in standard form. b. 2xy – 5y = 6 Since the term 2xy has two variables, the equation cannot be written in the form Ax + By = C. Therefore, this is not a linear equation.

4
**Identify Linear Equations**

Determine whether each equation is a linear equation. If so, write the equation in standard form. c. 3x + 9y = 15 Since the GCF of 3, 9, and 15 is not 1, the equation is not written in standard form. Divide each side by the GCF. 3x + 9y = 15 3(x + 3y) = 15 x + 3y = 5 The equation is now in standard form where A = 1, B = 3, and C = 5.

5
**Identify Linear Equations**

Determine whether each equation is a linear equation. If so, write the equation in standard form. d. 1/3 y = -1 To write the equation with integer coefficients, multiply each term by 3. 1/3 y = -1 3(1 /3 ) y = 3(-1) y = -3 The equation y = -3 can be written as 0x + y = -3. Therefore, it is a linear equation in standard form where A = 0, B = 1, and C = -3.

6
**Graph Linear Equations**

The graph of a linear equation is a line. The line represents all the solutions of the linear equation. Also, every ordered pair on this line satisfies the equation.

7
**Graph by Making a Table Graph x + 2y = 6.**

In order to find values for y more easily, solve the equation for y. x + 2y = 6 x + 2y – x = 6 – x 2y = 6 – x y = 3 – ½ x

8
Graph by Making a Table

9
Intercepts Since two points determine a line, a simple method of graphing a linear equation is to find the points where the graph crosses the x-axis and the y-axis. The x-coordinate of the point at which it crosses the x-axis is the x-intercept, and the y-coordinate of the point at which the graph crosses the y-axis is called the y-intercept.

10
**Graph Using Intercepts**

Determine the x-intercept and y-intercept of 3x + 2y = 9. Then graph the equation. To find the x-intercept, let y = 0. 3x + 2y = 9 3x + 2(0) = 9 3x = 9 x = 3

11
**Graph Using Intercepts**

Determine the x-intercept and y-intercept of 3x + 2y = 9. Then graph the equation. To find the y-intercept, let x = 0. 3x + 2y = 9 3(0) + 2y = 9 2y = 9 y = 4.5

12
**Graph Using Intercepts**

The x-intercept is 3, so the graph intersects the x-axis at (3 , 0). The y-intercept is 4.5, so the graph intersects the y-axis is (0 , 4.5). Plot these points. Then draw a line that connects them.

Similar presentations

© 2020 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google