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Chapter 4
Study Guide
Math 101
- Make time in your schedule to learn; you cannot take shortcuts.
- Read each section in your textbook and answer the questions in the study guide before you go to class.
- Take notes in class, trying to understand as the teacher presents examples and explains concepts.
- Do your homework (It should be easier after the previous two steps). Make sure to understand what you are doing and be able to solve each problem completely and correctly by yourself.
- Carry on a conversation with yourself as you work, asking as you start each problem, “What is this? What is my goal? What should my answer look like when I am done?” Then, as you work a problem ask, “What property allows me to take this step?” And at the end, “ Does my answer make sense? How can I check it?”
- Maintain a great attitude about learning Algebra; people who have a good attitude find it easier to learn, and those who learn algebra well usually enjoy it.
- Go to the lab or your instructor’s office and get help when you need it.
Section 4.1 Ordered Pairs and Graphs Read section 4.1, pages 202– 208 and answer the following questions as you read:
- Draw a rectangular coordinate system, label the origin, the axes, the quadrants, and the following ordered pairs: (2, 3), (2, -3), (-2, 3), and (-2, -3). Use a ruler to make your work neat.
- Why are the pairs of numbers called ordered pairs?
- Ordered pairs can be solutions of equations. How many variables must an equation have in order to have solutions that are ordered pairs?
- When is an ordered pair a solution to an equation?
- Is the ordered pair (-1, -2) a solution to the equation 2x-3y=4? Show how you know.
- Is the ordered pair (4, 2) a solution to the equation x-4y=7? Show how you know.
- Sketch the graph of 2x + y = -4 following example 1. Show your work on the left and write the steps you take on the right.
Need graph
- How do we know when an equation in two variables is a linear equation?
- Graph the equation having absolute value. Y = |x+2|
X -5 -4 -3 -2 -1 0 1
Y=|x+2|
Need graph
- Write two note cards: one with the definition of the x-intercept and one with the definition of y-intercept. Be sure to include a graph and an example.
- Explain, in complete sentences, why we let x=0 when we want to find the y-intercept and y=0 when we want to find the x-intercept. Does this work for equations whose graphs are not lines?
- Find the x and y intercepts of 2x+3y=6. Write your answers as ordered pairs and label which is the x-intercept and which is the y- intercept.
- Summarize what you learned in this section. Use complete sentences.
*While doing your homework, pick three problems (of different types) that you either couldn’t do by yourself or you found very hard and list them on the last page of this booklet.
Section 4.3 Relations, Functions, and Graphs Read section 4.3, pages 223 – 228 and answer the following questions as you read:
- Make four notecards with definitions: one for relations, one for function, one for domain, and one for range. Be sure to include an example on each card.
Section 4.4 Slope and Graphs of Linear Equations Read section 4.4, pages 234 - 241 and answer the following questions as you read:
- Make a note card for the word slope. Include the verbal definition, the formula, and a graph. Include an example of how the slope is
found. Also, include that the slope is arate of change.
- a. In example 1a, the slope is a positive number. Describe the direction the line is going as you look at it from left to right.
b. In example 1b, the slope is zero; describe the steepness of the line.
b. In example 1c, the slope is a negative number. Describe the direction the line is going as you look at it from left to right.
- What type of line has an undefined slope? Why?
- Make a note card for slope-intercept form of the equation of a line. Be sure to include what m and b mean, and how you can sketch a line once you know m and b.
- Make a note card for parallel lines. Describe how you can tell whether two lines are parallel. Include a graph and an example.
- Make a note card for perpendicular lines. Describe how you can tell whether two lines are perpendicular. Include a graph and an example.
- Use an illustration to summarize what you learned this section and how the concepts are related.
*While doing your homework, pick three problems (of different types) that you either couldn’t do by yourself or you found very hard and list them on the last page of this booklet.
Section 4.5 Equations of Lines Read section 4.5, pages 246 - 252 and answer the following questions as you read:
- Describe what is meant by Analytic Geometry.
- In example 1, you are asked to find the equation of a line when you are given the slope and one point. Say we knew the equation; what do you know about the relationship between the point and the equation?
- Make a note card for point-slope form of the equation of a line. Include an example and give steps for finding the equation of a line using this form when you have been given a slope and a point.
- If you are given two points instead of a slope and one point, what additional step do you have to take to find the equation?
- How is information from the last section used in examples 4 and 5?
- Give the equation of the horizontal line through (1,4).
- Study example 7 and then work this similar problem. During the first year of operation, a company had sales of $72 million. During the third year, the company had sales of $82 million. Using this information only and assuming this trend continues, what would you estimate the sales to be during the fifth year? The seventh year? Solution:
What shouldy represent?
What shouldt represent?
What should the horizontal axis of the graph represent? What should the vertical axis of the graph represent? Give two ordered pairs (t, y) from the statement of the problem.
Find the slope of the line containing the two points you gave.
Use the _______________________ form of the equation of a line to find the equation that gives the relationship between years and total sales.
Using this model, find the estimate of sales during the fifth year.
Use the model again to find the estimate of sales during the seventh year.
- You have learned two forms of the equation of a line. What are they?
a. Which one is most convenient for finding an equation?
b. Which one is most convenient for graphing a line?
*While doing your homework, pick three problems (of different types) that you either couldn’t do by yourself or you found very hard and list them on the last page of this booklet.
Section 4.6 Graphs of Linear Inequalities Read section 4.6, pages 257 - 261 and answer the following questions as you read:
- Make a note card for linear inequality in two variables. Include what a solution to a linear inequality in two variables is.
- Decide whether the point (-2, -3) is a solution to the linear inequality in example 1. Show your work.
- Write the steps for graphing a linear inequality in two variables. Include how you can check your solution.
- Give one solution for x>-2 from the graph of example 2a.
Find a solution in your graphed solution set and describe what it means.
Chapter 4 Review List the problems from each section here. Ask study partners to see problems they listed; if they are different types than you have listed below, copy theirs. Use this list as a practice test a couple of days before your chapter 4 test.
