Download Honors Unit 2

Unit Summary
Class : Algebra 1 Honors
Unit 2: Linear Functions – Chapter 6
I. Big Ideas:
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Students will understand how to use linear functions to model real world phenomena and solve
problems arising from those situations.
Students will understand how to translate among verbal, tabular, graphical, and algebraic
representations of functions.
Students will understand how to describe how slope and y-intercept appear in different
representations.
Students will understand that a linear function has infinitely many solutions that form a line.
II. Topics that will be covered:
1. Writing expressions for the nth term
2. Rate of change
3. Defining slope
4. Graphing the equation of a line
5. Horizontal and vertical lines
6. Writing the equation of a line
7. Converting between standard form and slope-intercept form
8. Using the slope-intercept form for the equation of a line
9. Parallel lines
10. Perpendicular lines
11. X and y intercepts
12. Line of best fit
13. Scatter plot
14. Solving linear equations
15. Domain, range, and functions
16. Collinear
III.
Essential Questions:
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How does a graph relate to the equation of a line?
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What does it mean to be a linear function?
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In what ways can a linear graph be used to interpret data and find solutions?
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How can we create and solve linear systems to model real world situations?
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How can I use graphs to describe relationships?
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What do intercept x and y intercepts mean?
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How do I know if a point is a solution to an equation?
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What does it mean to have a positive, negative, zero, or undefined slope?
IV.
Sample questions to answer by the end of the unit:
Write an equation for each table of values.
1.
x
y
-3
5
-2
11
-1
17
0
23
1
29
2
35
3
41
x
y
-3
30
-2
26
-1
22
0
18
1
14
2
10
3
6
2.
3. The table below shows the amount that a company charges for a raft rental for up to 10 hours. An initial
deposit is included in the amounts shown. Write an equation for the function.
Time (x) 2
Cost (y) 20
4
30
6
40
8
50
10
60
A) How much does the company charge per hour?
B) What is the initial deposit fee?
4. Which point is on the graph of the equation 3x + 6y = 27?
A. (0,9)
B. (5,2)
C. (1,-5)
D. (-5,7)
5. If y varies directly as x and y = 2/3 when x = ½, find an equation of direct variation.
A. y = 3/4x
B. y = -4/3x
C. y = 4/3x
D. y = -3/4x
6. An equation for the line that crosses the x-axis at x = -1 and y-axis at y = 3 is
A. 3x + y = 3
B. 3x = y + 3
C. y = 3x + 3
D. y + 3x = -3
7. Which line represents a horizontal line?
A. y = x
B. y = -2
C. x = 0
D. y = 2x + 1
8. The Smiths bought a house in 1975 for $90,000. In 1987, they sold it for $174,000. Assume that the
increase in value was constant over this period. Let t = 0 in 1975.
 Write an equation for the value V of the house at any time t.

Determine its value in 1989.
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When was its value $126,000?
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What is the slope and what does it mean in the context of this problem?
Convert from standard form to slope intercept.
9. 4x – 3y = 12
10. –8x + 2y = 14
Write an equation of each line in slope-intercept form.
11. A line with a slope of –4 and y-intercept of 16.
12. A line passing through (6, 0) and with y-intercept of 7.
13. A line containing the points (1, 5) and (3, 17).
14. A line passing through the origin and parallel to y = 7X + 6.
Write an equation for the line that contains the point (1, 5) and is:
15. parallel to y = 2x – 1
16. perpendicular to y = 2x – 1
Graph the following two equations on the same coordinate grid.
17. y = 3/5x – 2
18. y = -4X – 3