5.4 Write Linear Equations in
Standard Form
•Students will write equations in standard
form.
•Students will do assigned homework.
•Students will study
vocabulary words.
Lesson 5.4, For use with pages 311-316
Write an equation in point-slope form of the line that
passes through the given points.
1. (1, 4), (6, –1)
ANSWER
y – 4 = –(x – 1) or y + 1 = –(x – 6)
2. ( –1, –2), (2, 7)
ANSWER
y + 2 = 3(x + 1) or y – 7 = 3(x – 2)
Lesson 5.4, For use with pages 311-316
3. A store rents 3 DVDs for $5, plus $3 for each
additional DVD. Find the cost of renting 20 DVDs.
ANSWER
$56
Daily Homework Quiz
1.
Write an equation in point-slope form of the line
that passes through (6, –4) and has slope 2.
ANSWER
2.
For use after Lesson 5.3
y + 4 = –2(x – 6)
Write an equation in point-slope form of the line
that passes through (–1, –6) and (3, 10).
ANSWER
y + 6 = 4(x + 1) or y –10 = 4(x–3)
Daily Homework Quiz
3.
For use after Lesson 5.3
A travel company offers guided rafting trips for
$875 for the first three days and $235 for each
additional day. Write an equation that gives the
total cost (in dollars) of a rafting trip as a function
of the length of the trip. Find the cost for a 7-day
trip.
ANSWER
C = 235t + 170, where C is total cost and t is time
(in days); $1815
EXAMPLE 1
Write equivalent equations in standard form
Write two equations in standard form that are equivalent
to 2x – 6y = 4.
SOLUTION
To write one equivalent
equation, multiply each
side by 2.
4x – 12y = 8
To write another equivalent
equation, multiply each side
by 0.5.
x – 3y = 2
EXAMPLE 2
Write an equation from a graph
Write an equation in standard form of the line shown.
SOLUTION
STEP 1
Calculate the slope.
1 – (–2)
3
m=
= –1 = –3
1–2
STEP 2
Write an equation in point-slope form. Use (1, 1).
y – y1 = m(x – x1)
y – 1 = –3(x – 1)
Write point-slope form.
Substitute 1 for y1, 3 for m
and 1 for x1.
EXAMPLE 2
Write an equation from a graph
STEP 3
Rewrite the equation in standard form.
3x + y = 4
Simplify. Collect variable
terms on one side,
constants on the other.
EXAMPLE
1
GUIDED PRACTICE
for Examples 1 and 2
1. Write two equations in standard form that are
equivalent to x – y = 3.
ANSWER
2x – 2y = 6, 3x – 3y = 9
from 1a and
graph
EXAMPLE
2 Write an equation
for Examples
2
GUIDED PRACTICE
2. Write an equation in standard form of the line
through (3, –1) and (2, –3).
ANSWER
–2x + y = –7
EXAMPLE 3
Write an equation of a line
Write an equation of the specified line.
a.
Blue line
b.
Red line
SOLUTION
a.
b.
The y-coordinate of the given point on the blue
line is –4. This means that all points on the line
have a y-coordinate of –4. An equation of the
line is y = –4.
The x-coordinate of the given point on the red
line is 4. This means that all points on the line
have an x-coordinate of 4. An equation of the
line is x = 4.
EXAMPLE 4
3
Complete an equation in standard form
Find the missing coefficient in the equation of the line
shown. Write the completed equation.
SOLUTION
STEP 1
Find the value of A. Substitute the
coordinates of the given point for x and y in
the equation. Solve for A.
Ax + 3y = 2
A(–1) + 3(0) = 2
–A = 2
A = –2
Write equation.
Substitute –1 for x and 0 for y.
Simplify.
Divide by –1.
EXAMPLE 4
Complete an equation in standard form
STEP 2
Complete the equation.
–2x + 3y = 2
Substitute –2 for A.
GUIDED PRACTICE
for Examples 3 and 4
Write equations of the horizontal and vertical lines that
pass through the given point.
3.
(–8, –9)
ANSWER
y = –9, x = –8
GUIDED PRACTICE
for Examples 3 and 4
Write equations of the horizontal and vertical lines that
pass through the given point.
4.
(13, –5)
ANSWER
y = –5, x = 13
an
equation
standard
form
EXAMPLE
4
3 Complete
for
Examples
3 in
and
4
Write an
equation
of
a line
GUIDED PRACTICE
Find the missing coefficient in the equation of the
line that passes through the given point. Write the
completed equation.
5.
–4x + By = 7, (–1, 1)
ANSWER
3; –4x + 3y = 7
an
equation
standard
form
EXAMPLE
4
3 Complete
for
Examples
3 in
and
4
Write an
equation
of
a line
GUIDED PRACTICE
Find the missing coefficient in the equation of the
line that passes through the given point. Write the
completed equation.
6.
Ax + y = –3, (2, 11)
ANSWER
–7; –7x +y = –3
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.
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.
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
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.
aa multi-step
problem
EXAMPLE
5 Solve
for
Example
5
GUIDED
PRACTICE
Solve
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.
ANSWER
8s + 12l = 136; 17 small, 0 large; 14 small, 2 large; 11
small, 4 large; 8 small, 6 large; 5 small, 8 large; 2
small, 10 large