Name: Chapter 4: Equations of Linear Functions Lesson 4-1 ...simonclps.weebly.com/uploads/2/2/6/9/22693662/a1_notes_4.pdf · ... Chapter 4: Equations of Linear ... Lesson 4-2: Writing

Name: Chapter 4: Equations of Linear Functions

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Lesson 4-1: Graphing Equations in Slope-Intercept Form Date:

Example 1: Write an equation in slope-intercept form for each line from the bell ringer.

To graph an equation in slope-intercept form:

Step 1: Plot the y-intercept (0, 𝑏).

Step 2: From the y-intercept, use your slope. Recall: 𝑚 =𝑟𝑖𝑠𝑒

𝑟𝑢𝑛

Step 3: Draw a line through the two points.

Step 4: Label the equation

Example 2: Graph 5𝑥 + 4𝑦 = 8. Then state the domain and range.


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Example 3: Graph 𝑦 = −7. Then state the domain and range.

Example 4: Write an equation in slope-intercept form for the line shown in the graph.

Example 5: HEALTH The ideal maximum heart rate for a 25-year-old exercising to burn fat is 117 beats per minute. For every 5 years older than 25, that ideal rate drops 3 beats per minute.

A. Write a linear equation to find the ideal maximum heart rate for anyone over 25 who is exercising to burn fat.

B. Find the ideal maximum heart rate for a 55-year-old person exercising to burn fat.

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Lesson 4-2: Writing Equations in Slope-Intercept Form Date:

Writing an equation in slope-intercept form when given the slope and a point

Step 1: Start with 𝑦 = 𝑚𝑥 + 𝑏

Step 2: Substitute 𝑥 and 𝑦 using the given ordered pair.

Step 3: Substitute the slope, 𝑚.

Step 4: Solve for 𝑏.

Step 5: Rewrite 𝑦 = 𝑚𝑥 + 𝑏

Step 6: Substitute 𝑚 and 𝑏.

Example 1: Write an equation of a line that passes through (2, −3) with a slope of 1

2.

Writing an equation in slope-intercept form when given two points

Step 1: Find the slope using the given points.

Step 2: Choose one of the two points.

Step 3: Follow the steps for: Writing an equation in slope-intercept form when given the slope

and a point.

Example 2: Write the equation of the line that passes through (−3, −4) and (−2, −8).


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In mathematics a is a condition that a solution must satisfy. Equations can be

viewed as constraints in a problem situation. The solutions of the equation must meet the constraints of

the problem.

Example 3: ECONOMY During one year, Malik’s cost for self-serve regular gasoline was $3.20 on the first

of June and $3.42 on the first of July. Write a linear equation to predict Malik’s cost of gasoline the first of

any month during the year, using 1 to represent January.

You can use a linear equation to make predictions about values that are beyond the range of the data.

This process is called linear .

Example 4: ECONOMY On average, Malik uses 25 gallons of gasoline per month. He budgeted $100 for

gasoline in October. Use the prediction equation in Example 3 to determine if Malik will have to add to his

budget. Explain.


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Lesson 4-3: Writing Equations in Point-Slope Form Date:

To graph an equation in point-slope form:

Step 1: Plot the given point.

Step 2: From there, use your slope. Recall: 𝑚 =𝑟𝑖𝑠𝑒

𝑟𝑢𝑛

Step 3: Draw a line through the two points.

Step 4: Label the equation

Writing an equation in point-slope form given the slope and one point:

Step 1: Start with 𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1).

Step 2: Substitute 𝑥1 and 𝑦1 using the given point.

Step 3: Substitute the slope, 𝑚.

Writing an equation in point-slope form given two points:

Step 1: Find the slope using the given points.

Step 2: Choose one of the two points.

Step 3: Follow the steps for: Writing an equation in point-slope form given the slope and one point


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Example 1:

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

2.

Then graph the equation.

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

Then graph the equation.

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What is the standard form of a linear equation?

What is the slope-intercept form of a linear equation?

Example 2: Write 𝑦 + 1 =3

4𝑥 − 5 in standard form.

Example 3: Write 𝑦 − 5 =4

3(𝑥 − 3) in slope-intercept form.

Example 4: The figure shows right triangle 𝐴𝐵𝐶. Write the point-slope form of the line containing the

hypotenuse 𝐴𝐵̅̅ ̅̅ .


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Lesson 4-4: Parallel and Perpendicular Lines Date:

Example 1: Write the slope-intercept form of an equation for the line that passes through (4, – 2) and is

parallel to the graph of 𝑦 =1

2𝑥 − 7.

Example 2:

A. GEOMETRY The height of a trapezoid is the length of a segment that is

perpendicular to both bases. In trapezoid ARTP, 𝑅𝑇̅̅ ̅̅ and 𝐴𝑃̅̅ ̅̅ are bases. Can 𝐸𝑍̅̅̅̅ be used

to measure the height of the trapezoid? Explain.

B. Are the bases parallel?


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Example 3: Determine whether the graphs of 3𝑥 + 𝑦 = 12, 𝑦 = −1

3𝑥 + 2, and 2𝑥 – 6𝑦 = – 5 are parallel or

perpendicular. Explain.

Example 4: Write an equation in slope-intercept form for the line that passes through (4, –1) and is perpendicular to

the graph of 7𝑥 – 2𝑦 = 3.

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Lesson 4-5: Scatter Plots and Lines of Fit Date:

A shows the relationship between a set of data with two

variables, graphed as ordered pairs on a coordinate plane. They are used to investigate a relationship between

two quantities.

Example 1: TECHNOLOGY The graph shows the average number of students per computer in Maria’s

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

a positive or negative correlation, describe its meaning in the situation.

Scatter plots can show whether there is a trend in the set of data.

When the data points all lie close to a line, a can model the trend.

Using a linear function to model data:

Step 1: Make a scatter plot. Determine whether any relationship exists.

Step 2: Draw a line that seems to pass close to most of the data points.

Step 3: Use two points on the line of fit to write an equation for the line.

Step 4: Use the line of fit to make predictions


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Example 2: POPULATION The table shows the world population growing at a rapid rate. Identify the

independent and dependent variables. Make a scatter plot and determine what relationship, if any, exists in

the data.

Recall: Linear is used to predict values outside the range of data.

Linear is used to predict vales inside the range of data.

Example 3: The table and graph show the world population growing at a rapid rate. Use the equation

y = 35.1x – 63,870 to predict the world’s population in 2025. Is this an example of linear extrapolation or

linear interpolation?

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Lesson 4-6: Regression and Median Fit Lines Date:

Example 1: EARNINGS The table shows Ariana’s hourly earnings for the years 2001–2007. Use a graphing

calculator to write an equation for the best-fit line for the data. Name the correlation coefficient. Round to

the nearest ten-thousandth.

Example 2: BOWLING The table shows the points earned by the top ten bowlers in a tournament. How

many points did the 15th-ranked bowler earn?

Example 3: Find and graph the equation of a median-fit line for the data on the bowling tournament in the

table. Then predict the score of the 20th-ranked bowler.


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Lesson 4-7: Inverse Linear Functions Date:

Example 1: Find the inverse of each relation.

A. {(−3, 26), (2, 11), (6, −1), (−1, 20)} B.

Example 2: Graph the inverse of each relation.

A. B.


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Example 3: Find the inverse of each function.

A. 𝑓 (𝑥) = – 3𝑥 + 27 B. 𝑓(𝑥) =5

4𝑥 − 8

Example 4: SALES Carter sells paper supplies and makes a base salary of $2200 each month. He also earns

5% commission on his total sales. His total earnings f(x) for a month in which he compiled x dollars in total

sales is f(x) = 2200 + 0.05x.

A. Find the inverse function.

B. What do x and f –1(x )represent in the context of the inverse function?

C. Find Carter’s total sales for last month if his earnings for that month were $3450.

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Name: Chapter 4: Equations of Linear Functions Lesson 4-1 ...simonclps.weebly.com/uploads/2/2/6/9/22693662/a1_notes_4.pdf · ... Chapter 4: Equations of Linear ... Lesson 4-2: Writing