Solving Equations & Inequalities
Solve for x:
3x - 5 = 1
x = 2
What is the slope-intercept formula and what does each part of the formula represent?
slope-intercept formula:
y = mx + b
labels: 'm' is the slope, 'b' is the y-intercept, 'x' is the input, and 'y' is the output
Solve using Substitution, write your answer as an ordered pair:
{(y = 4), (2x + y = 10):}
(3, 4)
Explain the difference between an arithmetic sequence and a geometric sequence
An arithmetic sequence has terms that add or subtract by the same amount (common difference)
A geometric sequence has terms that multiply or divide by the same factor (common ration)
Solve for x:
4x+7=2x+15
x = 4
Fill in the blank:
- Parallel lines have the ________ slope
- Perpendicular linear have slopes that are ______ of each other
- Parallel lines have the __same__ slope
- Perpendicular linear have slopes that are _negative reciprocals__ of each other
Solve using Elimination, write your answer as an ordered pair:
{(2x + 2y = 14), ( 2x - 2y = 2):}
(4,3)
2) create a geometric sequence and list the common ratio
answers my vary, will be checked manually by the teacher
1) When do you flip the inequality sign?
2) Solve the inequality for x, write the solution in interval notation, and graph your solution using a number line:
-2(3x-4) <= x+8
1) Whenever you MULTIPLY OR DIVIDE by a NEGATIVE number
2) Solution: x >= 0 ; graph will be checked by hand
1) Write the equation of a line in slope-intercept form given: slope m=−2 and y-intercept (0,5)
2) graph the line and label the y-intercept
1) y = -2x + 5
2) graph will be checked by hand
Solve using Substitution, write your answer as an ordered pair:
{(y=2x+3), (3x-y=4):}
(7, 17)
1) Determine whether the situation is best modeled by a linear or exponential function: A savings account balance increases by 5% each year.
2) Construct a function P(t) for a population that increases by 20% every year and the initial population is 200.
1) the situation is best modeled by an exponential function
2) P(t) = 200 * (1+0.2)^X
Solve the absolute value equation and check all solutions:
|4x-2| = 14
The solutions are x = -3 and x = 4 . Can also be written as x = -3, 4
Determine whether the relation represented by the ordered pairs {(1,2),(2,5),(3,8),(4,11)} is a function.
Explain your reasoning.
Yes it is a function because the points pass the vertical line test. In other words, each input has only one output mapped to it
Graph the solution set of the system of inequalities:
{(y≤2x+1) , (y>−x+4):}
Shade the correct region and label the lines appropriately (solid/dashed)
graph checked by hand
- there should be 1 solid and 1 dashed boundary line
Given the function y=2*3^x, plot 3 points and sketch the graph.
Then write the new equation if the original equation was vertically shifted down by 5.
plot will be checked by hand
New equation will be: y = 2*3^x -5