(8) Lesson 3.6

1. Course 3, Lesson 3-6
Use the guess, check, and revise strategy to solve each exercise.
1. The product of two consecutive odd integers is 3,363. What are the
integers?
2. Jorge decided to buy a souvenir keychain for $2.25, a cup for $2.95,
or a pen for $1.75 for each of his 9 friends. If he spent $22.05 on
these souvenirs and bought at least one of each type of souvenir, how
many of each did he buy?
3. A number squared is 729. Find the number.
4. Candace has $2.30 in quarters, dimes, and nickels in her change
purse. If she has a total of 19 coins, how many of each coin does she
have?

2. Course 3, Lesson 3-6
ANSWERS
1. 57 and 59
2. 3 key chains, 4 cups, 2 pens
3. 27
4. 6 quarters, 3 dimes, 10 nickels

3. WHY are graphs helpful?
Expressions and Equations
Course 3, Lesson 3-6

4. • Preparation for 8.EE.8c
Solve real-world and mathematical problems leading to two linear equations in
two variables.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
5 Use appropriate tools strategically.
7 Look for and make use of structure.
Course 3, Lesson 3-6 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council
of Chief State School Officers. All rights reserved.
Expressions and Equations

5. To
• write equations in point-slope form
• write equations in slope-intercept form
Course 3, Lesson 3-6
Expressions and Equations

6. • point-slope form
Course 3, Lesson 3-6
Expressions and Equations

7. Course 3, Lesson 3-6
Expressions and Equations
Words The linear equation
is written in point-slope form, where
is a given point on a
nonvertical line and m is the slope
of the line.
Symbols
1 1
( )y y m x x  
1 1
( , )x y
1 1
( )y xmy x  
Graph

8. 1
Need Another Example?
2
3
Step-by-Step Example
1. Write an equation in point-slope form for the line that passes
through (–2, 3) with a slope of 4.
y – y1 = m(x – x1) Point-slope form
y – 3 = 4[x – (–2)] (x1, y1) = (–2, 3), m = 4
y – 3 = 4(x + 2) Simplify.

9. Answer
Need Another Example?
Write the point-slope form of an equation for a
line that passes through (2, 4) with slope – .

10. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
2. Rewrite the equation y − 3 = 4(x + 2) in slope-intercept form.
y – 3 = 4(x + 2) Write the equation.
y – 3 = 4x + 8 Distributive Property
y = 4x + 11 Simplify.
Addition Property of Equality
Check: Substitute the coordinates of the given point
in the equation.
y = 4x + 11
3 = 4(–2) + 11
3 = 3
?
+ 3 = + 3

11. Answer
Need Another Example?
Rewrite the equation y – 4 = – (x – 2) in
slope-intercept form.

12. Course 3, Lesson 3-6
Expressions and Equations
From Slope
and a Point
From Slope
and y-intercept
From a Graph
From Two
Points
From a Table
• Substitute the slope m and the coordinates of the point
in .
• Substitute the slope m and y-intercept b in y = mx + b.
• Find the y-intercept b and the slope m from the graph,
then substitute the slope and y-intercept in y = mx + b.
• Use the coordinates of the points to find the slope.
Substitute the slope and coordinates of one of the
points in .
• Use the coordinates of the two points to find the slope,
then substitute the slope and coordinates of one of
the points in .
1 1
( )y y m x x  
1 1
( )y y m x x  
1 1
( )y y m x x  

13. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
3. Write an equation in point-slope form and slope-intercept form
for the line that passes through (8, 1) and (–2, 9).
Find the slope.
Slope formula
Use the slope and the coordinates of either point to
write the equation in point-slope form.
Point-slope formy – y1 = m(x – x1)
Simplify.
(x1, y1) = (8, 1), m = –
(x1, y1) = (8, 1), (x2, y2) = (–2, 9)
So, the point-slope form of the equation is y – 1 = – (x – 8).
In slope-intercept form, this is y = – x + .

14. Answer
Need Another Example?
Write an equation in point-slope form and
slope-intercept form for the line that passes
through (3, 6) and (4, −2).
Sample answer: y – 6 = –8(x – 3); y = –8x + 30

15. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
4. The cost of assistance dog training sessions is
shown in the table. Write an equation in point-slope
form to represent the cost y of attending x dog
training sessions.
Find the slope of the line. Then use the slope
and one of the points to write the equation of the line.
(x2, y2) = (10, 290), (x1, y1) = (5, 165)
So, the equation of the line is y – 165 = 25(x – 5).
Replace (x1, y1) with (5, 165) and m with
25 in the point-slope form equation.
y – 165 = 25(x – 5)
Simplify.

16. Answer
Need Another Example?
The cost of different amounts of paper plates at
a party supply store is shown in the table. Write
an equation in point-slope form to represent the
cost y of buying x paper plates.

17. How did what you learned
today help you answer the
WHY are graphs helpful?
Course 3, Lesson 3-6
Expressions and Equations

18. How did what you learned
today help you answer the
WHY are graphs helpful?
Course 3, Lesson 3-6
Expressions and Equations
Sample answers:
• If you need to write an equation from a graph, you can
easily locate the y-intercept.
• You can find the slope of the line by counting to find
the rise and the run.

19. What is the equation in
point-slope form of the line
that passes through
(−2, 4) and (3, −1)?
Ratios and Proportional RelationshipsExpressions and Equations
Course 3, Lesson 3-6