SWBAT find the x-intercept and y-intercept of a linear relationship and explain its meaning.
Example 1: A high school student takes a job that pays a wage of $2 per hour, and he also gets a
signing bonus of $3.
A) Graph this relationship on the Cartesian plane.
B) What is the slope of the relationship? Explain how to find the slope in the equation, table, and graph.
Slope =
Equation:
Table:
Graph:
C) What is the meaning of the slope in the context of the story?
D) What is the y-intercept of the relationship? Explain how to find the y-intercept in the equation,
table, and graph.
Y-int. =
Equation:
Table:
Graph:
E) What is the meaning of the y-intercept in the context of the story?
NOTES:
Example 2: In high school you start up a lacrosse team. In order to get money for equipment and team
jerseys, you organize a potluck dinner fundraiser open to adults and students. Your goal is to sell $1600
worth of tickets. You assume that 200 adults and 100 students will attend the dinner, but you’re not
sure how much to charge for each ticket. What prices could you charge adults and students to make sure
you make your goal?
A) Write an equation to represent the situation and define your variables.
B) Find the x and y intercepts algebraically, and use the intercepts to create a graph.
C)
D)
E)
F)
What is the slope of the graph? What does it mean?
What is the y-intercept of the graph? What does it mean?
What is the “zero” of the graph? What does it mean?
What is another possible combination of prices?
Now You Try: Graph the equation y = 2x – 4 using the two methods that we have learned.
Method 1: Slope intercept form
Method 2: Find x and y-intercepts
A) Explain why your two graphs should be the same.
B) Which method do you like better? Explain.
You are running for Freshman Class President at your new high school. You have $60 to
spend on publicity. It costs $5 to make a campaign button, and $3 to make a poster.
Write an equation that represent the different numbers of buttons, x, and posters, y, that
you can make with your money.
Find the x and y intercepts of the equation:
Graph the situation below. Be sure to LABEL YOUR AXES.
(a) What does the x intercept represent in terms of the situation? Use complete sentences.
(b) If you make 15 posters, then how many buttons can you afford to make? Justify your
answer.
1. What is the slope of the graph? What does it mean?
2. What is the y-intercept of the graph?
What does it mean?
3. Graph the equation y = -3x + 6.
4. What is the slope of the graph? What is the y-intercept?
5. Find the x and y intercepts of the equation y = -10x + 50 algebraically. Show your work.
6. Find the x and y intercepts of the equation 3x + 5y = 30 algebraically. Show your work.
7. What is the slope of the equation in #6? (Solve for y to find the coefficient of x).
8. What are the coordinates of the point where 2x + y = 10 crosses the x-axis?
A) (0, 10)
B) (10, 0)
C) (0, 5)
D) (5, 0)
9. What is the slope of a line that passes through the points (8, 1) and (10, 13)?
10. Before 1979, there was no 3-pt shot in basketball; players could only score a 2pt field
goal, or a 1pt free throw. A game (before 1979) scored 44 points total.
a. Write an equation to represent the different amounts of 2pt field goals and 1pt free
throws that could have been scored during this game. (Define your variables)
b. Find the x and y intercepts of the equation:
c. Graph the situation. Be sure to LABEL YOUR AXES.
d. What does the y-intercept mean in this situation?
e. What are two possible numbers of field goals and free throws that could have been
scored?
f. If the team made 18 field goals, then how many free throws did they score?
11) Ms. Marriott is organizing an optional field trip for 8th graders and staff to see a play at
the Lincoln Center. She is able to get a discounted price on the tickets: student tickets are
$6 each, and adult tickets are $8 each. If Ms. Marriott has a budget of $240, then what
different combinations of students and adults can go on the trip?
Equation:
Define the variables:
Find the intercepts and then graph:
(a) If no students went, then how many adults could go?
(b) If no adults went, then how many students could go?
(c) If 32 students decided to go, then how many adults could go?