Algebra Lesson 3.5: Graphing Linear Equations Using Point-Slope Form

Practice Exercises:

Graph the following equations

1. \(y-3 = 2(x-1)\)

2. \(y - \frac{1}{3} = \frac{2}{3}(x-\frac{1}{2}\)

3. \(y - 1 = -\frac{5}{2}(x+1)\)

Use the following graph to answer Exercises 4 and 5

4. Write the equation of the red line in point-slope form using the indicated point.

5. Write the equation of the blue line in point-slope form using the indicated point.

Algebra Lesson 3.4: Graphing Vertical and Horizontal Lines

Practice Exercises:

For each of the following equations, decide whether the graph is a vertical line, horizontal line, or neither

1. \(x = 2\)

2. \(y = x\)

3. \(y= 1\)

Graph each of the following equations

4. \(y=\frac{1}{2}\)

5. \(x = -3\)

Use the following graph two answer Exercises 6 and 7

6. What is the equation of the vertical red line?

7. What is the equation of the horizontal green line?

Review Exercise:

8. Which of the two lines in the graph above is the graph of a function? (Review the vertical line test for functions)

Algebra Lesson 4.2: The Vertical Line Test

Practice Exercises:

For each of the following images use the vertical line test to decide whether or not the image is the graph of a function.

1.

2.

3.

4.

5.

6.

The Best Calculator for the SAT and Beyond

You're reading this post because you want to do well on the SAT, or you want your child to do well on the SAT. You want to have the best possible tools at your disposal to accomplish this goal, and you know that the right calculator is the most important tool for the math portion of the test.

I don't have to explain to you the importance of the SAT to your future options. You wouldn't be reading this post if you didn't already know that. All you need is for me to tell you what calculator is the best choice for the SAT, right?

Well, that depends. You may have already noticed the mile-long list of SAT-approved calculators. I'm here to tell you that you can throw that list away. If you don't already have a graphing calculator, you really only need to choose between two calculators, the TI-84 series or the TI-89 series.

Before I try to convince you that you really only need to choose between these two calculators, let me interject a huge caveat.  If you only have a few days before the test, this is no time to start thinking about a new calculator. Use what you are used to. You don't want to waste precious time on the test trying to figure out how to do simple calculations on a calculator that is not familiar to you. If your school classes use a specific type of graphing calculator, then make sure you have that kind for the test. Some schools actually allow students to check out calculators for use on the SAT.  Please, please, please don't use a calculator you haven't already used a lot before the test when you take the SAT. You do not want to waste valuable test time trying to figure out your calculator. To find out if your current calculator is allowed for use during the SAT, see the official list here: https://sat.collegeboard.org/register/calculator-policy.

I'll assume that those of you who have chosen to keep reading have more time to prepare for the test and therefore have time to familiarize yourselves with a new calculator.

A good calculator is a pretty big investment. No doubt you've seen the hefty prices and want to make sure you're getting the right one. You'll want a good graphing calculator, and those don't come cheap. On the other hand, if you choose the right one, it will most likely take you through your entire math career. So picking the right calculator in the first place can save you quite a bit of money in the long run. In order to pick the right calculator, you really only have to answer one question for yourself:

Will I be taking calculus?

If you are not planning on ever taking calculus. The TI-84 series becomes the obvious best choice for a calculator to buy and use on the SAT. It will take you through your entire math career. Your professors will most likely use this series of calculator for demonstrations in class.

On the other hand, if you plan to eventually take calculus, the TI-84 just isn't going to cut it. The TI-89 series becomes your best option. The TI-89 can do everything the TI-84 can do. On top of that it can do calculus, and it has a computer algebra system (CAS). This means a TI-89 can actually solve equations for you (and much more).

So it's that simple. If you plan to eventually take calculus, go with the TI-89 series. If you won't be taking calculus, go with the TI-84 series. You'll find that there are several versions of each of these calculators available. The latest calculator in the TI-84 series is the TI-84 Plus C Silver Edition Programmable Color Graphing Calculator (shop for this calculator at Amazon.com). But you really don't have to go with the latest edition. If you don't care about the color screen, any edition of the TI-84 will do. For the TI-89 series the latest edition is the TI-89 Titanium (shop for this calculator at Amazon.com). However, a regular old TI-89 will work just fine.

Once you choose which calculator is right for your situation, there are great tutorials available on Youtube, such as the videos by www.tiskills.com (visit Youtube channel page).

TI-84 Series:                                     TI-89 Series:

                             

Algebra Lesson 3.2: Graphing a Linear Equation Using Intercepts

Practice Exercises:

Find the \(x\) and \(y\) intercepts of the given equation and use them to make a graph of the equation.

1. \(2x + 3y = 6\)

2. \(5x - 6y = 10\)

3. \(x + 2y = 3\)

You can use this same method to graph equations of lines that are not written in standard form. Find the \(x\) and \(y\) intercepts of the given equation and use them to make a graph of the equation.

4. \(-\frac{2}{3}x + 2y = 3\)

5. \(y = 4x -2\)

6. \(2x = 3y + 4\)

Algebra Lesson 3.3: Graphing using Slope-Intercept Form

Practice Exercises:

For each of the following equations, find the slope and the \(y\)-intercept. Then use these to graph the equation.

1. \(y = 4x -1\)

2. \(y = \frac{2}{3} + 3\)

3. \(y = x +4\)

Use the following graph to answer Exercises 4-6

4. Write the equation of the red line in slope-intercept form.

5. Write the equation of the blue line in slope-intercept form.

6. Write the equation of the green line in slope-intercept form.

Algebra Lesson 2.9: Writing Linear Equations in Standard Form

Practice Exercises

Rewrite the following equations in standard form

1. \(-2x + y = 7\)

2. \(\frac{1}{3}x + 2y = \frac{4}{3}\)

3. \(-\frac{7}{4}x - 2y = \frac{1}{8}x\)

The following equations are given in slope-intercept form. Rewrite them in standard form

4. \(y = -2x + 2\)

5. \(y = \frac{1}{2}x + 1\)

6. \(y = 6x + 5\)

Use the following graph to answer Exercises 7-9

7. Write the equation of the line passing through points A and B in point-slope form (review how to do this). Then rewrite the equation in standard form.

8. Write the equation of the line passing through points B and C in point-slope form. Then rewrite the equation in standard form.