Download Study Guide for “Moving Straight Ahead”

Answers to Study Guide for “Moving Straight Ahead”
1. Given one of the representations below, find the other two.
Table
Graph (each box is 1 unit per side)
Equation
i.
ii.
y= x+1
iii.
a. Find the y-intercept for each representation above.
i. __________
ii.____________
iii._____________
b. Find the slope for each representation above.
i. _________
ii. ____________
Answer:
Table
iii. ______________
Graph
Equation
y = –3x + 8
y = 4x – 3
y= x+1
2. Gretchen was absent when the class developed strategies for solving linear equations.
Write an explanation to her about how to solve equations. Use the equation
4n – 17 = 43 as an example.
Answer: You can think of solving an equation like this one as reversing the procedure that was
done to create the expression on the left. To make 4n – 17 you would multiply n by 4 and then
subtract 17. To reverse this, you add 17, then divide by 4.
3. a.This table shows two points that are on the same straight line. Complete the table to
show three other points on the same line.
Answer:
x
-3
-2
-1
0
1
y
-2
0
2
4
6
b. Find the slope and the y-intercept of this line that represents the data. Write the
equation. slope
, y-intercept
; equation: y = 2x + 4
4. Here is a graph of three lines.
a. Complete the chart.
line
constant rate of change
(slope)
y-intercept
A
B
C
b. Here are the equations of the three lines. Match each line with its equation.
,
,
line A: ____________, line B: ____________, line C: ____________
Answer: The equation for the line labeled A: y = 3 – x;
the equation for the line labeled B: y = 2 + x; the equation for the line labeled C: y = – 4 + 2x
a.
line
A
B
C
b. line A: y = 3 – x,
constant rate of change
–1
1
2
y-intercept
(0, 3)
(0, 2)
(0, –4)
line B: y = 2 + x, line C: y = –4 + 2x
5. The equations below represent the costs to print brochures at three different printers.
a. For which equation does the point (20, 60) lie on the graph? Explain.
i.
C = $15 + $2.50N
ii. C = $50 + $1.75N
iii. C = $30 + $1.50N
Answer: a. Equation iii because the point satisfies the equation: 60 = 30 + 1.5(20).
6. Find the number described in each problem by writing and solving an equation.
a. If Sarah subtracts five times her number from 24, she gets 4. What is Sarah's
number?
Answer: a. 24 – 5x = 4; 4
c. The sum of 4 times a number and 4 is 16. What is the number?
Answer: 4x + 4 = 16; 3
7. Solve the following equations for the value of x:
a. 3x + 5 = 4x – 10
b. 4x + 10 = 6x – 8
a. x = 15
b.
c. 3x + 10 = 5x
d. 3x – 11 = 8x – 21
c. x = 5
d.
x=9
x=2
e. 3(x + 8) = 12
e. x = –4
8. Find the slope and y-intercept of the line represented by each equation.
a. y = 7x + 1
slope is 7; y-intercept is (0, 1)
c. y = 4x
slope is 4; y-intercept is (0,0)
b. y = 5 - 2x
slope is –2; y-intercept is (0, 5)
d. y = -3x – 8
slope is –3; y=intercept is (0, -8)