Name:
Date:
Algebra 2
Review: Linear Functions
Review Outline

Linear function formulas
y 2 - y1
or a table or a graph
x 2 - x1
o Point-slope form f(x) = m(x – h) + k
o Slope-intercept form f(x) = mx + b
Graphs of linear functions
o Graphing point-slope and slope-intercept lines, using a starting point and the slope
o Horizontal lines (y = #) and vertical lines (x = #)
o Parallel lines (equal slopes) and perpendicular lines (opposite reciprocal slopes)
Evaluating and solving
o Given an input, finding an output (evaluating)
o Given an output, finding an input (solving equations)
o Solving inequalities and double inequalities
Modeling (application) problems
o Meaning of slope: a rate or a speed
o Turning word problems into function formulas
o Domain and range
o Evaluating/solving (see above) and giving the meaning of the answer in the problem
context
 Finding Equations for Best Fit Lines
o Identifying and explaining the correlation coefficient (r).
o Finding the slope using m =



Review Problems
1. Write function formulas for these lines, using the coordinates of the marked point in your
formula.
a. f(x) = ______________________
b. f(x) = ______________________
Name:
Date:
Algebra 2
2. Graph these equations.
a. x = –3
b. y = –3
3. Answer these questions about the function f(x) = - 13 ( x - 1) + 2.
a. Evaluate f(4).
b. Solve f(x) = 4.
c. Find the zero(s) of f(x).
d. Find the y-intercept of f(x).
e. Graph f(x) on the grid.
c. y = –3x
Name:
Date:
Algebra 2
4. A car is driving down from the top of a Colorado mountain. The elevation at the top of the
mountain is 13,500 feet. Every minute of driving, the car’s elevation decreases by 150 feet.
Let x = the time in minutes that the car has been driving down the mountain,
E(x) = the car’s elevation in feet.
a. Write a function formula equation for E(x).
b. Evaluate E(5), and explain the meaning of the answer in terms of the car.
c. Find the answer by setting up and solving an equation: There is a scenic overlook at
elevation 12,300 feet. How much time will it take the car to reach the scenic overlook?
d. Find the answer by setting up and solving an inequality: The top of the mountain is too
cold for trees to grow, but below 11,700 feet there are trees. When will the car be on the
part of the mountain that has trees?
e. Find the answer by setting up and solving an inequality: The part of the mountain
between 9,000 feet and 12,000 feet is in the subalpine climate zone. When will the car be
in the subalpine climate zone?
f. Suppose that the car drive ends at a mountain lodge with an elevation of 7,500 feet.
What are the domain and range of function E(x)?
Name:
Date:
5. A cereal is sold in boxes of different sizes. Suppose that
the price of a box is a linear function of the weight. The
prices for boxes of three sizes are shown in the table.
Let P(x) stand for the price of an x ounce box of cereal.
a. Find a function formula for P(x).
Algebra 2
weight
(in ounces)
14
18
26
price
(in dollars)
2.59
2.99
3.79
Find answer to the following questions using your function formula from part a. Show work.
b. What would be the price for a 21-ounce box of cereal?
c. What would be the weight for a cereal box that costs $4.99?
d. Find P(0), and explain what this number means in terms of the cereal pricing.
Name:
Date:
Algebra 2
6. Write linear equations using the given information.
a. The table below represents a linear equation. Write a formula for f(x).
x
f(x)
5
4
7
1
9
-2
11
-5
b. The table below represents a linear equation. Write a formula for f(x).
x
f(x)
5
4
7
4
9
4
11
4
c. The table below represents a linear equation. Write a formula for y.
x
y
4
5
4
7
4
9
4
11
Name:
Date:
Algebra 2
d. Write the equation of a line perpendicular to y = 2(x + 3) – 4 that goes through (1, 5).
e. Write the equation of any line parallel to y = 2(x + 3) – 4.
f. Write the equation of the line perpendicular to f(x) = 5 that goes through (-1, -3).
g. Write the equations of the line parallel to f(x) = 5 that goes through (-1, -3)
7. Let L be the line whose graph is shown on the grid.
a. Write an equation for line L.
b. Write an equation for a line that is parallel to L
and goes through point (–3, 2). Also graph this
line on the grid.
c. Write an equation for a line that is perpendicular to L and goes through point (–3, 2).
Also graph this line on the grid.
Name:
Date:
Algebra 2
8. a. Enter this table into your calculator in columns L1 and L2 .
b. Use your calculator to find the best-fit line equation. Write down
the equation.
x
3
5
6
7
8
y
4
12
15
22
27
c. Write down the correlation number r from the calculator. What does it tell you about how
well the line fits the data?
d. Graph the data points and the best-fit line together on your
calculator screen. (If you don’t see five points and a line,
try pressing [ZOOM][9] to fix.) Draw your calculator
screen.
Answers to Review Problems
1. a. y = – 34 x – 6
2. a. vertical
b. y =
1
2
(x + 3) – 5
c. slope of –3
b. horizontal
3. a. f(4) = 1 b. x = –5 c. x = 7 d. f(0) =
7
3
e. see graph
Name:
Date:
Algebra 2
MORE ANSWERS
4. a. E(x) = –150x + 13500.
b. E(5) = 12750. After 5 minutes, car is at 12,750 feet.
c. x = 8. After 8 minutes, car is at 12,300 feet.
d. E(x) < 11700  x > 12, so after more than 12 minutes.
e. 9000 ≤ E(x) ≤ 12000  10 ≤ x ≤ 30, so in the
subalpine zone between 10 minutes and 30 minutes.
f. First solve E(x) = 7500 to get x = 40.
Domain: 0 ≤ x ≤ 40; Range: 7500 ≤ E(x) ≤ 13500.
5. a. P(x) = 0.10(x – 14) + 2.59, or you may have used a different point. b. P(21) = 3.29
c. 38 ounces
d. P(0) = 1.19, base price reflecting packaging
3
6a. f ( x) = - ( x - 5) + 4
b. f(x) = 4
c. x = 4
2
1
d. f ( x) = - ( x -1) + 5
2
e. f ( x) = 2x + b (pick any number for b. or, choose any point and plug into point-slope form.)
f. x = -1
g. y = -3
7. a. Using the point (5, 1): y = 13 (x – 5) + 1. Or you may have used a different point.
b. y =
1
3
(x + 3) + 2.
c. y = –3(x + 3) + 2.
8b. y = 4.595x - 10.649
c. r = .99. Tells you the best - fit line is a good match to the points and that the slope is positive.