3%2D1 Graphing Linear Equations

[Pages:51]3-1 Graphing Linear Equations

Determine whether each equation is a linear equation. Write yes or no. If yes, write the equation in standard form. x = y ? 5 62/87,21 Rewrite the equation in standard form.

The equation is now in standard form where A = 1, B = ?1, and C = ?5. This is a linear equation.

?2x ? 3 = y 62/87,21 Rewrite the equation in standard form.

The equation is now in standard form where A = 2, B = 1, and C = ?3. This is a linear equation.

?4y + 6 = 2

62/87,21 Rewrite the equation in standard form.

The equation is now in standard form where A = 0, B = 1, and C = 1. This is a linear equation.

eSolutions Manual - Powered by Cognero

Page 1

3-1 G raphing Linear Equations The equation is now in standard form where A = 0, B = 1, and C = 1. This is a linear equation.

62/87,21 Rewrite the equation in standard form.

The equation is now in standard form where A = 2, B = ?1, and C = 6. This is a linear equation. Find the x- and y -intercepts of the graph of each linear function. Describe what the intercepts mean.

62/87,21

The x-intercept is the point at which the y -coordinate is 0, or the line crosses the x-axis. So, the x-intercept is 25. The y -intercept is the point at which the x-coordinate is 0, or the line crosses the y -axis. So, the y -intercept is ?4. The x-LQWHUFHSWPHDQVWKDWDIWHUPLQXWHVWKHWHPSHUDWXUHLV)7KHy-intercept ?4 means that at time 0, the temperature is ?)

62/87,21

The x-intercept is the point at which the y -coordinate is 0, or the line crosses at the x-axis. So, the x-intercept is 12. The y -intercept is the point at which the x-coordinate is 0, or the line crosses at the y -axis. So, the y -intercept is ?24. The x-intercept 12 means that after 12 seconds, the scuba diver is at a depth of 0 meters, or at the surface. The yintercept ?24 means that at time 0, the scuba diver is at a depth of ?24 meters, or 24 meters below sea level.

eSolutGionrsaMpahnueaalc-hPoewqeureadtbioy nCobgyneurosing the x- and y -intercepts. y = 4 + x

62/87,21

Page 2

62/87,21 The x-intercept is the point at which the y -coordinate is 0, or the line crosses at the x-axis. So, the x-intercept is 12. The y -intercept is the point at which the x-coordinate is 0, or the line crosses at the y -axis. So, the y -intercept is ?24. 3-1 GTrhaepxh-intgerLcienpeta1r2Emqeuaantsiotnhast after 12 seconds, the scuba diver is at a depth of 0 meters, or at the surface. The yintercept ?24 means that at time 0, the scuba diver is at a depth of ?24 meters, or 24 meters below sea level. Graph each equation by using the x- and y -intercepts. y = 4 + x 62/87,21 To find the x-intercept, let y = 0.

To find the y -intercept, let x = 0.

So, the x-intercept is ?4, and the y -intercept is 4. Plot these two points and then draw a line through them.

2x ? 5y = 1

62/87,21 To find the x-intercept, let y = 0.

To find the y -intercept, let x = 0.

eSolutions Manual - Powered by Cognero

Page 3

3-1 Graphing Linear Equations

2x ? 5y = 1 62/87,21 To find the x-intercept, let y = 0.

To find the y -intercept, let x = 0.

So, the x-intercept is , and the y-intercept is

. Plot these two points, and then draw a line through them.

Graph each equation by making a table. x + 2y = 4

62/87,21 Solve for y.

eSolutions Manual - Powered by Cognero

Select values from the domain and make a table. Create ordered pairs and graph them.

Page 4

3-1 Graphing Linear Equations

Graph each equation by making a table. x + 2y = 4

62/87,21 Solve for y.

Select values from the domain and make a table. Create ordered pairs and graph them.

x

y

(x, y)

?4

4

(?4, 4)

?2

3

(?2, 3)

0

2

(0, 2)

2

1

(2, 1)

4

0

(4, 0)

?3 + 2y = ?5

62/87,21 Select values from the domain and make a table. Create ordered pairs and graph them.

eSolutions Manual - Powered by Cognero

Page 5

3-1 Graphing Linear Equations

?3 + 2y = ?5 62/87,21 Select values from the domain and make a table. Create ordered pairs and graph them.

y = 3

62/87,21 Select values from the domain and make a table. Create ordered pairs and graph them.

CCSS REASONING The equation 5x + 10y = 60 represents the number of children x and adults y who can attend

the rodeo for $60.

a. Use the x- and y-intercepts to graph the equation. b. Describe what these values mean. eSolut6io2ns/M8an7u,a2l -1Powered by Cognero

a. To find the x-intercept, let y = 0.

Page 6

3-1 Ga.raUpsheinthgeLxi-naenadryE-iqnuteartcieopntss to graph the equation. b. Describe what these values mean.

62/87,21 a. To find the x-intercept, let y = 0.

To find the y -intercept, let x = 0.

So the x-intercept is 12 and the y -intercept is 6. Plot these points, and then draw a line through them.

b. The x-intercept means that 12 children and 0 adults can attend for $60. The y -intercept means that 0 children and 6 adults can attend for $60.

Determine whether each equation is a linear equation. Write yes or no. If yes, write the equation in standard form. 5x + y2 = 25

62/87,21 Since y is squared, the equation cannot be written in standard form. So, the equation is not linear.

8 + y = 4x

62/87,21 Rewrite the equation in standard form. eSolutions Manual - Powered by Cognero

Page 7

5x + y2 = 25 62/87,21

3-1 GSrinacpehyinisg sLqiunaeraedr,Ethqeueaqtiuoantison cannot be written in standard form. So, the equation is not linear.

8 + y = 4x 62/87,21 Rewrite the equation in standard form.

The equation is now in standard form where A = 4, B = 1, and C = 8. 9xy ? 6x = 7 62/87,21 Since there are two variables in one term, the equation cannot be written in standard form. So, the equation is not linear. 4y2 + 9 = ?4 62/87,21 Since y is squared, the equation cannot be written in standard form. So, the equation is not linear. 12x = 7y ? 10y 62/87,21 Rewrite the equation in standard form.

The equation is now in standard form where A = 4, B = 1, and C = 0. y = 4x + x 62/87,21 Rewrite the equation in standard form.

eSolutions Manual - Powered by Cognero

The equation is now in standard form where A = 5, B = ?1, and C = 0.

Page 8

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download