Warm-Up
Write an equation in standard form of the line that passes
through the given point and has the given slope m or that
passes through the two given points.
1. (-5, -6), m = 3
2.
(– 4, – 3), (1, 6)
ANSWER
2x + y = – 4
ANSWER
– 2x + y = 5
3. Rewrite the equation in standard form with integer
coefficients.
a) 0.5x + 0.38y = 0.2
b) 2.3x + 0.283y = 3.28
5.6b Students will be able to use the standard form of linear equations to solve word problems.
Daily Homework Quiz
For use after Lesson 5.6
Write an equation in standard form of the line that passes
through the given point and has the given slope m.
1.
(1, – 6), m = – 2
ANSWER
2x - y = – 9
2. Rewrite the equation in standard form with integer
coefficients.
3.5x + 0.38y = 38
350x + 38y = 3800
5.6b Students will be able to use the standard form of linear equations to solve word problems.
EXAMPLE 5
Solve a multi-step problem
Library
Your class is taking a trip to the public library. You can
travel in small and large vans. A small van holds 8
people and a large van holds 12 people. Your class
could fill 15 small vans and 2 large vans.
a. Write an equation in standard form that models
the possible combinations of small vans and
large vans that your class could fill.
b. Graph the equation from part (a).
c. List several possible combinations.
5.6b Students will be able to use the standard form of linear equations to solve word problems.
EXAMPLE 5
Solve a multi-step problem
SOLUTION
a. Write a verbal model. Then write an equation.
8
s
+
12
p
l
=
Because your class could fill 15 small vans and 2
large vans, use (15, 2) as the s- and l-values to
substitute in the equation 8s + 12l = p to find the
value of p.
8(15) + 12(2) = p
Substitute 15 for s and 2 for l.
Simplify.
144 = p
Substitute 144 for p in the equation 8s + 12l = p.
5.6b Students will be able to use the standard form of linear equations to solve word problems.
EXAMPLE 5
Solve a multi-step problem
ANSWER
The equation 8s + 12l = 144 models the possible
combinations.
b.
Find the intercepts of the graph.
Substitute 0 for s.
8(0) + 12l = 144
l = 12
Substitute 0 for l.
8s + 12(0) = 144
s = 18
5.6b Students will be able to use the standard form of linear equations to solve word problems.
EXAMPLE 5
Solve a multi-step problem
Plot the points (0, 12) and (18, 0). Connect them
with a line segment. For this problem only
nonnegative whole-number values of s and l make
sense.
c. The graph passes through (0, 12), (6, 8),(12, 4), and
(18, 0). So, four possible combinations are 0 small
and 12 large, 6 small and 8 large, 12 small and 4
large, 18 small and 0 large.
5.6b Students will be able to use the standard form of linear equations to solve word problems.
a multi-step
problem
EXAMPLE
5 Solve
for
Example
5
GUIDED
PRACTICE
Solve
a
multi-step
problem
EXAMPLE 5
7. WHAT IF? In Example 5, suppose that 8 students
decide not to go on the class trip. Write an equation
that models the possible combinations of small and
large vans that your class could fill. List several
possible combinations.
5.6b Students will be able to use the standard form of linear equations to solve word problems.
a multi-step
problem
EXAMPLE
5 Solve
for
Example
5
GUIDED
PRACTICE
Solve
a
multi-step
problem
EXAMPLE 5
SOLUTION
STEP 1 Write a verbal model. Then write an equation.
8
s
+
12
p
l
=
8 students decide not to go on the class trip, so the
class could fill 14 small vans and 2 large vans. Because
your class could fill 14 small vans and 2 large vans, use
(14, 2) as the s- and l-values to substitute in the equation
8s + 12l = p to find the value of p.
8(14) + 12(2) = p
Substitute 14 for s and 2 for l.
Simplify.
136 = p
Substitute 136 for p in the equation 8s + 12l = p.
5.6b Students will be able to use the standard form of linear equations to solve word problems.
problem
EXAMPLE
5 Solve a multi-step
for Example
5
GUIDED PRACTICE
ANSWER
The equation 8s + 12l = 136 models the possible
combinations.
STEP 2 Find the intercepts of the graph.
Substitute 0 for s.
8(0) + 12l = 136
4
l = 11
12
Substitute 0 for l.
8s + 12(0) = 136
s = 17
5.6b Students will be able to use the standard form of linear equations to solve word problems.
GUIDED PRACTICE
for Example 5
Plot the point(0,11 4 )and(17, 0).connect them with
12
a line segment. For this problem only negative
whole-number values of s and l make sense.
STEP 3
The graph passes through (17, 0), (14, 2), (11, 4),
(8, 6), (5, 8) and (2, 10). So, several combinations
are 17 small, 0 large; 14 small 2 large; 11 small,
4 large; 18 small, 6 large; 5 small, 8 large; 2 small,
10 large.
5.6b Students will be able to use the standard form of linear equations to solve word problems.
Daily Homework Quiz
3.
For use after Lesson 5.4
You have $96 to spend on campground activities.
You can rent a paddleboat for $8 per hour and a
kayak for $6 per hour. Write an equation in
standard form that models the possible hourly
combinations of activities you can afford. List
three possible combinations.
ANSWER
8p + 6c = 96;
16 h kayak and 0 h paddleboat;
12 h paddleboat and 0 h kayak;
6 h paddleboat and 8 h kayak.
5.6b Students will be able to use the standard form of linear equations to solve word problems.