1. 4-6 Writing Linear Equations for Word Problems
Give a problem that has y-intercept like in the
sample problem. Problems in alignment with
handout.
Algebra Glencoe McGraw-Hill Linda Stamper

2. There are two basic types of real-life problems that can be solved with linear equations.
Type I Problems involving a constant rate of change (slope).
(Write equation in slope-intercept form.)

3. There are two basic types of real-life problems that can be solved with linear equations.
Type I Problems involving a constant rate of change (slope).
(Write equation in slope-intercept form.)
Type II Problems involving two variables, x and y, such that the
sum of Ax + By is a constant.
(Write equation in standard form.)

4. What is the equation of this line?
You open a savings account with $150. You plan to add $50 each month. Write an equation that gives the monthly savings, y (in dollars), in terms of the month, x. y
No graph is given.
(5,400) •
Can you visualize the graph in your head?
(3,300) •
savings (dollars)
If the y-intercept is not given, what piece of information would you need? •
100
a point 50 x
If the slope is not given, what information would you need? 1 2
months
What is the equation of this line?
two points

5. Between 1980 and 1990, the monthly rent for a one-bedroom apartment increased by $40 per year. In 1985, the rent was $300 per month. Write an equation that gives the monthly rent y (in dollars), in terms of the year x. Let year 0 correspond to 1980.

6. Between 1980 and 1990, the monthly rent for a one-bedroom apartment increased by $40 per year. In 1985, the rent was $300 per month. Write an equation that gives the monthly rent y (in dollars), in terms of the year x. Let year 0 correspond to 1980.
Assign Labels:
Let x = years Let y = monthly rent in dollars
Find the constant rate of change (slope).
Think of a point on the graph that represents 1985 and $300. y
Write an equation.
(5,300) •
rent (dollars) x
years
1980

7. Recall value problems.
Andrea has 52 coins in dimes and quarters worth $10. How many of each coin does she have?
Number Labels
and Value Labels
Let d = number of dimes
Let 52 – d = number quarters
Let .10d = value of the dimes
Let .25(52 – d) = value of quarters
Verbal Model.
Value of dimes + Value of quarters = Total Value
Write the equation.
.10d (52 – d) = 10
Today you will write a linear equation that has two variables to represent a word problem.
Type II Problems involving two variables, x and y, such that the sum of Ax + By is a constant.

8. Mrs. Burke’s drama class is presenting a play next Friday night and you have been put in charge of ticket sales. Tickets for adults are sold for $4 each and students pay $2 each. Write a linear equation, in standard form, that models the different number of adult tickets, x, and the number of student tickets, y, that could be sold if total ticket sales are $320.

9. Mrs. Burke’s drama class is presenting a play next Friday night and you have been put in charge of ticket sales. Tickets for adults are sold for $4 each and students pay $2 each. Write a linear equation, in standard form, that models the different number of adult tickets, x, and the number of student tickets, y, that could be sold if total ticket sales are $320.
Number Labels
and Value Labels
Let x = number of adult tickets
Let y = number of student tickets
Let 4x = value of adult tickets
Let 2y = value of student tickets
Verbal model.
Value of adult + value of student = total value of
tickets tickets tickets
Write the equation.

10. Example 1 Between 1980 and 1990, the monthly rent for a one-bedroom apartment increased by $20 per year. In 1987, the rent was $350 per month. Write an equation that gives the monthly rent y (in dollars), in terms of the year x. Let year 0 correspond to 1980.

11. Example 1 Between 1980 and 1990, the monthly rent for a one-bedroom apartment increased by $20 per year. In 1987, the rent was $350 per month. Write an equation that gives the monthly rent y (in dollars), in terms of the year x. Let year 0 correspond to 1980.
Assign Labels
Let x = years Let y = monthly rent in dollars
Find the constant rate of change (slope).
Think of a point on the graph that represents 1987 and $350. y
Write an equation.
(7,350) •
rent (dollars) x
years
1980

12. Example 2 You are flying from LA to Boston
Example 2 You are flying from LA to Boston. Three hours into the trip you have traveled 825 miles. You are traveling at an average speed of 275 mph. Write a linear equation that gives the distance y (in miles), after x hours of flying.

13. Example 2 You are flying from LA to Boston
Example 2 You are flying from LA to Boston. Three hours into the trip you have traveled 825 miles. You are traveling at an average speed of 275 mph. Write a linear equation that gives the distance y (in miles), after x hours of flying.
Assign Labels
Let x = hours flying Let y = distance in miles
Find the constant rate of change (slope).
Think of the point on a graph that represents 3hrs and 825 mi. y
Use point-slope to write an equation.
distance •
(3,825) x
hours

14. Example 3 By the end of your 5th French lesson you have learned 20 vocabulary words. After 10 lessons you know 40 vocabulary words. Write an equation that gives the number of vocabulary words you know y, in terms of the number of lessons you have had x.
Assign Labels
Let x = # lessons Let y = # vocab. words
Find the slope.
Write an equation.

15. Example 4 Joan earns $4 an hour when she works on Fridays, and $6 an hour on Saturdays. Write a linear equation that models the different number of hours she could have worked on each of the two days if she earned $36. If x (Friday’s hours) and y (Saturday’s hours) are whole number, find all the possible combinations she could have worked on Friday and Saturday.

16. Example 4 Joan earns $4 an hour when she works on Fridays, and $6 an hour on Saturdays. Write a linear equation that models the different number of hours she could have worked on each of the two days if she earned $36. If x (Friday’s hours) and y (Saturday’s hours) are whole number, find all the possible combinations she could have worked on Friday and Saturday.
Assign number labels.
Let x = Fri. hours Let y = Sat. hours
Assign earning labels.
Let 4x = Fri. earn. Let 6y = Sat. earn.
Verbal model.
Friday’s earn. + Saturday’s earn. = total earn.
Write the equation.

17. Example 4 Joan earns $4 an hour when she works on Fridays, and $6 an hour on Saturdays. Write a linear equation that models the different number of hours she could have worked on each of the two days if she earned $36. If x (Friday’s hours) and y (Saturday’s hours) are whole number, find all the possible combinations she could have worked on Friday and Saturday. y
Make a table. x y
Sat. hours
(0,6) • •
(3,4)
(6,2) •
(9,0) • x
Friday hours

18. Example 5 You want to buy some CDs and Videos for the Teen Center recreation room. You have $75 to spend. You can order CDs for $15 each and Videos for $5 each from your discount catalog. Write a linear equation that models the different number of CDs and Videos you could purchase. If x (number of CDs) and y (number of Videos) are whole numbers, find all the possible combinations you could purchase.
Assign # labels.
Let x = # CDs Let y = # Videos
Assign cost labels.
Let 15x = cost of CDs Let 5y = cost of Videos
Verbal model.
Cost of CDs + Cost of Videos = total cost
Write the equation.

19. • • • • • • x Make a table and graph. y
# of Videos • • x
# of CDs
The ordered pairs represent the possible combinations.
(0,15), (5,0), (1,12), (2,9), (3,6), (4,3)

20. Practice 1 You collect comic books. In 1990 you had 60 comic books
Practice 1 You collect comic books. In 1990 you had 60 comic books. By the year 2000 you had 240 comic books. Find an equation that gives the number of comic books y, in terms of the year, x. Let year 0 correspond to 1990.
Practice 2 Maria decides to start jogging every day at the track. The first week she jogs 4 laps. She plans to increase her laps by one lap per week. Let y represent the number of laps Maria runs and let x represent the number of weeks she’s running. Write a linear equation that gives the number of laps she is running after x weeks.

21. Practice 1 You collect comic books. In 1990 you had 60 comic books
Practice 1 You collect comic books. In 1990 you had 60 comic books. By the year 2000 you had 240 comic books. Find an equation that gives the number of comic books y, in terms of the year, x. Let year 0 correspond to 1990.
Assign Labels
Let x = year Let y = # comic books
Identify two points.
Use slope-intercept to write an equation.

22. Practice 2 Maria decides to start jogging every day at the track
Practice 2 Maria decides to start jogging every day at the track. The first week she jogs 4 laps. She plans to increase her laps by one lap per week. Let y represent the number of laps Maria runs and let x represent the number of weeks she’s running. Write a linear equation that gives the number of laps she is running after x weeks.
Assign Labels
Let x = # weeks Let y = # laps
Find the slope.
Identify a point.
Use point-slope to write an equation.

23. Homework
4-A13 Handout A13