• point-slope form

• Write the equation of a line in point-slope form.

• Write linear equations in different forms.

Write an Equation Given Slope and a Point

(x1, y1) = (–2, 0)

Point-slopeform

Simplify.

Answer:

Write the point-slope form of an

equation for a line that passes

through (–2, 0) with slope

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. y – 4 = –2 (x + 3)

B. y + 3 = –2 (x – 4)

C. y – 3 = –2 (x – 4)

D. y + 4 = –2 (x – 3)

Write the point-slope form of an equation for a line that passes through (4, –3) with slope –2.

Write an Equation of a Horizontal Line

Write the point-slope form of an equation for a horizontal line that passes through (0, 5).

Answer: The equation is y – 5 = 0.

(x1, y1) = (0, 5)

Point-slopeform

Simplify.

y – 5 = 0 (x – 0)

y – y1 = m(x – x1)

y – 5 = 0

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. y + 4 = 0

B. y + 3 = 0

C. y – 4 = 0

D. x + 3 = 0

Write the point-slope form of an equation for a horizontal line that passes through (–3, –4).

Write an Equation in Standard Form

In standard form, the variables are on the left side of the equation. A, B, and C are all integers.

Multiply each side by 4 to eliminate the fraction.

Original equation

Distributive Property

Write an Equation in Standard Form

4y – 3x = 3x – 20 – 3x

–3x + 4y = –20

Answer: The standard form of the equation is –3x + 4y = –20 or 3x – 4y = 20.

Simplify.

Subtract 3x from each side.

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. –2x + y = 5

B. –2x + y = 7

C. –2x + y = 11

D. 2x + y = 11

Write y – 3 = 2(x + 4) in standard form.

Write an Equation in Slope-Intercept Form

Distributive Property

Original equation

Add 5 to each side.

Simplify.

Write an Equation in Slope-Intercept Form

Answer: The slope-intercept form of the equation is

A. A

B. B

C. C

D. D

A B C D

0% 0%0%0%

Write 3x + 2y = 6 in slope-intercept form.

A.

B. y = –3x + 6

C. y = –3x + 3

D. y = 2x + 3

Write the point-slope form of the lines containing the bases of the trapezoid.

Write an Equation in Point-Slope Form

A. GEOMETRY The figure shows trapezoid ABCD with bases AB and CD.

Write an Equation in Point-Slope Form

Step 1 First find the slopes of AB and CD.

(x1, y1) = (–2, 3)

(x2, y2) = (4, 3)

Slope formula

Slope formula

(x1, y1) = (1, –2)

(x2, y2) = (6, –2)

AB:

CD:

Step 2 You can use either point for (x1, y1) in the point-slope form.

Write an Equation in Point-Slope Form

Method 1 Use (–2, 3).AB: Method 2 Use (4, 3).AB:

y – y1 = m(x – x1)

y – 3 = 0(x + 2)

y – 3 = 0

y – y1 = m(x – x1)

y – 3 = 0(x – 4)

y – 3 = 0

Write an Equation in Point-Slope Form

Answer: The point-slope form of the equation containing AB is y – 3 = 0. The point-slope form of the equation containing CD is y + 2 = 0.

CD: Method 1 Use (1, –2). CD: Method 2 Use (6, –2).

y – y1 = m(x – x1)

y + 2 = 0(x – 1)

y + 2 = 0

y – y1 = m(x – x1)

y + 2 = 0(x – 6)

y + 2 = 0

B. Write each equation in standard form.

Answer: y = –2

Write an Equation in Point-Slope Form

Answer: y = 3

Original equation

Add 3 to each side.

Simplify.

Original equation

Subtract 2 from each side

Simplify.

AB: y – 3 = 0

y – 3 + 3 = 0 + 3

CD: y + 2 = 0

y + 2 – 2 = 0 – 2

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. y – 6 = 1(x – 4)

B. y – 1 = 1(x – 3)

C. y + 4 = 1(x + 6)

D. y – 4 = 1(x – 6)

A. The figure shows right triangle ABC. Write the point-slope form of the line containing the hypotenuse AB.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. –x + y = 10

B. –x + y = 3

C. –x + y = –2

D. x – y = 2

B. The figure shows right triangle ABC. Write the equation in standard form of the line containing the hypotenuse.

http://www.tx.algebra1.com/

Five-Minute Check (over Lesson 4-5)

Main Ideas and Vocabulary

Targeted TEKS

Key Concept: Scatter Plots

Example 1: Analyze Scatter Plots

Example 2: Find a Line of Fit

Example 3: Linear Interpolation

• scatter plot

• positive correlation• negative correlation• line of fit• best-fit line• linear interpolation

• Interpret points on a scatter plot.

• Use lines of fit to make and evaluate predictions.

TECHNOLOGY Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe it.

Answer: The graph shows a negative correlation. With each year, more computers are in Maria’s school, making the students-per-computer rate smaller.

Analyze Scatter Plots

The graph shows the average students per computer in Maria’s school.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. Positive correlation; with each year, the number of mail-order prescriptions has increased.

B. Negative correlaton; with each year, the number of mail-order prescriptions has decreased.

C. No correlation

D. Cannot be determined

Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe it.

The graph shows the number of mail-order prescriptions.

POPULATION The table shows the world population growing at a rapid rate.

Find a Line of Fit

Interactive Lab:Analyzing Linear Equations

A. Draw a scatter plot and determine what relationship exists, if any, in the data.

Let the independent variable x be the year and let the dependent variable y be the population (in millions).

The scatter plot seems to indicate that as the year increases, the population increases. There is a positive correlation between the two variables.

Find a Line of Fit

B. Draw a line of fit for the scatter plot.

No one line will pass through all of the data points. Draw a line that passes close to the points. A line is shown in the scatter plot.

Find a Line of Fit

C. Write the slope-intercept form of an equation for equation for the line of fit.

The line of fit shown passes through the data points (1850, 1000) and (2004, 6400).

Find a Line of Fit

Step 1 Find the slope.

Slope formula

Let (x1, y1) = (1850, 1000) and (x2, y2) = (2004, 6400)

Simplify.

Step 2 Use m = 35.1 and either the point-slope form or the slope-intercept form to write the equation. You can use either data point. We chose (1850, 1000).

Find a Line of Fit

Point-slope form

y – y1 = m(x – x1)

y – 1000 35.1x – 64,935)

y – 1000 35.1 (x – 1850)

y 35.1x – 63,935

Find a Line of Fit

Slope-intercept form

y = mx + b

1000 64,935 + b

1000 = 35.1 (1850) + b

–63,935 b

y 35.1x – 63,935

Answer: The equation of the line is y 35.1 – 63,935.

1. A

2. B

3. C

4. D

The table shows the number of bachelor’s degrees received since 1988.

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. There is a positive correlation between the two variables.

B. There is a negative correlation between the two variables.

C. There is no correlation between the two variables.

D. Cannot be determined

A. Draw a scatter plot and determine what relationship exists, if any, in the data.

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. B.

C. D.

B. Draw a line of best fit for the scatter plot.

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. y = 8x + 1137

B. y = –8x + 1104

C. y = 6x + 47

D. y = 8x + 1104

C. Write the slope-intercept form of an equation for the line of fit.

Use the prediction equation y 35.1x – 63,935, where x is the year and y is the population (in millions), to predict the world population in 2010.

Answer: 6,616,000,000

Linear Interpolation

y 35.1x – 63,935

y 6616

y 35.1 (2010) – 63,935

Original equation

Simplify.

Replace x with 2010.

1. A

2. B

3. C

4. D

0%0%0%0%

A B C D

A. 1,204,000

B. 1,104,000

C. 1,104,008

D. 1,264,000

Use the equation y = 8x + 1104, where x is the years since 1998 and y is the number of bachelor’s degrees (in thousands), to predict the number of bachelor’s degrees that will be received in 2015.