1. Course 3, Lesson 3-4
For Exercises 1–2, refer to the graph.
1. The amount of money Aisha earns
varies directly with the number of hours
she works at the bookstore. What is the
ratio of money earned to hours worked?
2. Continuing at the rate shown, how much
will Aisha have earned after working 21
hours?
3. Determine whether the linear function given in the table is a direct
variation. If so, state the constant of variation.
6. To
• determine the slope and y-intercept
of a graph
• write an equation of a line in slope-
intercept form
Course 3, Lesson 3-4
Expressions and Equations
8. 1
Need Another Example?
2
3
Step-by-Step Example
1. State the slope and the y-intercept of the graph of the
equation y = x – 4.
The slope of the graph is , and the y-intercept is –4.
y = mx + b
Write the equation in the form y = mx + b.
m = , b = –4
10. Need Another Example?
Step-by-Step Example
2. Write an equation of a line in slope-intercept form
with a slope of –3 and a y-intercept of –4.
1
2
3 y = –3x – 4
y = mx + b Slope-intercept form
Replace m with –3 and b with –4.y = –3x + (–4)
Simplify.
12. 1
Need Another Example?
2
3
4
Step-by-Step Example
3. Write an equation in slope-intercept
form for the graph shown.
y = – x + 4
The y-intercept is 4. From (0, 4), you
move down 1 unit and right 2 units to
another point on the line.
Slope-intercept formy = mx + b
Replace m with – and b with 4
So, the slope is – .
14. 1
Need Another Example?
2
3
Step-by-Step Example
4. Student Council is selling T-shirts during spirit week. It costs
$20 for the design and $5 to print each shirt. The cost y to
print x shirts is given by y = 5x + 20. Graph y = 5x + 20 using
the slope and y-intercept.
Find the slope and y-intercept.
y = 5x + 20 slope = 5
y-intercept = 20
Write the slope 5 as . Use it to locate a second point on
the line. Go up 5 units and right 1 unit. Then draw a line
through the points.
Graph the y-intercept (0, 20).
16. 1
Need Another Example?
Step-by-Step Example
5. Student Council is selling T-shirts during spirit week.
It costs $20 for the design and $5 to print each shirt.
The cost y to print x shirts is given by y = 5x + 20.
Interpret the slope and y-intercept.
The slope 5 represents the cost in dollars per T-shirt. The
y-intercept 20 is the one-time charge in dollars for the
design.
17. Answer
Need Another Example?
A kayak rental pavilion charges $15.00 per hour
and $2.50 for a brief lesson on kayak safety. The
total cost y to rent the kayak for x hours is given
by y = 15x + 2.5. Interpret the slope and y-intercept.
The slope 15 represents the rate of change or
cost per hour. The y-intercept 2.5 is the charge
for instruction.
18. How did what you learned
today help you answer the
WHY are graphs helpful?
Course 3, Lesson 3-4
Expressions and Equations
19. How did what you learned
today help you answer the
WHY are graphs helpful?
Course 3, Lesson 3-4
Expressions and Equations
Sample answers:
• If a nonproportional linear relationship is graphed, you
can easily determine the slope and y-intercept.
• When the relationship is graphed, you can interpret the
slope and y-intercept.
20. Explain how you would
graph y = –14x + 3
using the slope and
y-intercept.
Ratios and Proportional RelationshipsExpressions and Equations
Course 3, Lesson 3-4