Download Algebra B

Algebra B
Unit 7 – Linear Relationships
Name ___________________________
Date ______________Period_________
What’s the Equation of the line?
y = mx + b
Previously, you developed ways to find the growth of a line using its rule, table, and graph. You
also learned how the y-intercept is present in each of the multiple representations. In this chapter,
you will complete your study of lines and will develop ways to find the equation of a line using
different pieces of information about the line, such as two points that are on it.
Today’s lesson will help you review connections you made in previous chapters by challenging
your to find equations for lines from multiple representations.
1.
GETTING TO KNOW YOU, Part Three
Your teacher will give you a card with a representation of a line (a table, graph, rule, or
situation). Consider what you know about the line represented on your card. Then find
the other students in your class that have a representation of the same line. These
students will be your teammates. Be prepared to justify how you know your
representation matches those of your teammates.
2.
THE LINE FACTORY, Part One
Congratulations! You have recently been hired to work at the city’s premiere Line
Factory. People from all over the country order lines from your factory because of their
superior quality and excellent price.
However, lately the Line Factory is having a serious problem: Too many customers have
places orders and then received a line different from the one they wanted! The factory
has hired your team to eliminate this problem.
Your Task: Review the recent orders (the bulleted items that follow) and decide if there
is anything wrong with each customer’s order. If the order is correct, then pass it on to
your production department with a rule, a table, and a graph (on graph paper). However,
if the order is incorrect, explain to the customer how you know the order is incorrect and
suggest corrections.

Customer A want a line that has y-intercept at (0, -3) and grows by 4. She
ordered the line y = -3x + 4.

Customer B wants the line graphed at right.
He ordered the line y = 3x + 2.
7-1

Customer C wants a line that passes through the points (2, -4) and (5, 2). She
ordered the line y = 2x – 8.

Customer D wants the line that is represented by the table below.

Customer E ordered the line 2x – y = 4 and wants the line to grow by 2 and pass
through the point (5, 6).

Customer F wants a line that starts at (0, 1), grows first by 3 and then grows by 5.
Review/Preview
Examine the tile pattern shown at right.
1. Draw Figure 0 and Figure 4.
2. How many tiles will Figure 10 have? Justify your answer.
3. Match each system of equations in the left column with its solution in the right column.
a.
6x – y = 4
3x + y = 5
1.
(0, - 4)
b.
x=y+4
3x + y = 5
2.
(3, 7)
c.
5x – 2y = 1
y = 2x + 1
3.
(1, 2)
4. Use proportional reasoning to solve each of the problems below.
a. At the zoo, three adult lions eat 250 pounds of food a day. If two more adult
lions joined the group, how much food would the zoo need to provide each day?
b. Byron can read 45 pages in an hour. How long will it take him to read the new
700-page Terry Cotter book?
5. Graph y  
1
x  6 . Find its x- and y-intercepts.
2
6. Solve each equation below for the indicated variable.
a. 4x – 2 + y = 6 – 2x for y
b. 4x – 2 + y = 6 – 2x for x
c. 3(6 – x) + 2x = 15 for x
7. Little Evan has 356 stuffed animals, all of which are either teddy bears or dogs.
He has 17 more than twice as many dogs as teddy bears. How many teddy bears
does he own? Write and solve a system of equations to solve this problem. Be
sure to define your variables.