Algebra I: Equations, Inequalities, and Functions
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Algebra I Review
Inequalities
What happens to the inequality sign if you multiply or divide by a negative number?
Flip the inequality symbol
Which part of the inequality sign determines when you have a closed circle on a graph?
The line under the symbol. (Equal to line)
Domain is the _______ value of an ordered pair, which is also known as the _________ value.
x, independent
Range is the ______ value of an ordered pair, which is also known as the _______ value.
y, dependent
Linear Equations
What is the formula to find the slope of a line?
m = (y2 - y1) / (x2 - x1)
Write the equation of the point-slope form of a line.
y - y1 = m(x - x1)
Write the equation of the slope-intercept form of a line.
y = mx + b
Write the equation of the standard form of a line.
Ax + By = C
Solving Equations
z + 4 = -3
-7
y/4 = -6
-24
-5x = -35
7
(w - 3) / -4 = 2
-5
-18 = 9 - 3v
9
u / -3 + 6 = 14
-24
4t - 7 + 2 = -29
-6
-5s - 9 + 8s = 36
15
1 + 6r - 3 = 22
4
2(-q + 4) = -18
13
3(p - 1) + 2p = 7
2
1 - 3(3n + 1) = 25
-3
4m + 3 = 3m + 10
7
9l - 2 = 6l - 19
-17/3
Word Problems
After playing $5.50 for a salad at McDonald's, Ariel has $27.70. How much money did she have before buying the salad?
33.20
Buffalo Wild Wings charges $8.00 for 16 boneless wings on Thursday nights. Each dipping sauce costs an additional $.75. Wesley paid $10.25 for his wings and dipping sauces. How many dipping sauces did he order?
3
Inequalities and Functions
Rewrite the equation in slope-intercept form: 5x + 9y = 30
y = -5/9x + 10/3
Graph the inequality -2 > z
Open circle at -2 and shaded to the left
Write the inequality of the graph that has a closed circle at 1 and is shaded to the left.
x <= 1
Solve: The sum of a number p and 15 is less than 25.
p < 10
Write an inequality for: Cell phone plans are at most $15.00
x <= 15
5/8y < -10
y < -16
60 - 6x > 12
x < 8
2(w + 4) - 3w < 14
w > -6
5v + 6 - 3v <= -22
v <= -14
12 - 3u >= 3(4 - u)
Infinitely Many Solutions
You want to make a rectangular banner that is 16 feet long. You have no more than 50 feet of trim for the banner. What are the possible widths of the banner?
Maximum of 16 x 9
Your cell phone plan costs $39.99 per month plus $.20 for each text message you send or receive. You have at most $70 to spend on your cell phone bill. What is the maximum number of text messages that you can send or receive next month?
150
Look at question 37 on your study guide. What is the equation that represents the function in the table?
y = 6x + 14
Look at question 38 on your study guide. What is the equation that represents this function? Is it a direct variation?
y = x + 2, no
A sunflower plant in Darnell's garden was 2 feet tall when it was first planted. Since then, it has grown approximately 3 feet per month. Write an equation to represent this situation. How many months will the sunflower plant be 17 feet tall?
y = 3x + 2, 5
A Las Vegas taxi company charges passengers $4.00 for a ride and an additional $2.00 for each mile traveled. The function rule C = 2.00m + 4.00 describes the relationship between the number of miles m and the total cost of the ride c. If the taxi company will only go a maximum of 10 miles, construct a reasonable graph of the function rule.
y-intercept of 4 and a slope of 2.
What makes a relation a function?
Every input has exactly one output.
Describe the pattern and identify the next two terms:
9, 14, 19, 24, ...
pattern: + 5 next terms: 29, 34
Describe the pattern and identify the next two terms:
2, -6, 18, -54, ...
pattern: x 3 next terms: 162, -486