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 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.

Algebra Lesson 2.8: Find the Equation of a Line Given Two Points on the Line

Practice Exercises

Find the slope of the line passing through the two points given:

1. \((1,3)\) and \((0, 2)\)

2. \((4,1)\) and \((-2,3)\)

3. \((3,2)\) and \((4,5)\)

Find the equation of the line passing through the two points given:

4. \((1,1)\) and \((\frac{-1}{2},2)\)

5. \((0,0)\) and \((4,\frac{3}{2})\)

Use the following graph to answer Exercises 6 - 8

6. Find the equation of the line passing through points A and B

7. Find the equation of the line passing through points A and C

8. Find the equation of the line passing through the points B and C

Algebra Lesson 2.7: Finding the x and y Intercepts of a Linear Equation

Practice Exercises:

Find the \(x\) and \(y\) intercepts of the following equations:

1. \(x + 2y = 2\)

2. \(4x - 3 y = 7\)

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

4. \(y = 3x-4\)

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

Use the following graph to answer questions 6 and 7

6. Estimate the \(x\) and \(y\) intercepts of the green line.

7. Estimate the \(x\) and \(y\) intercepts of the blue line.

Algebra Lesson 2.6: Point-Slope Form

Practice Exercises

Write the equation of the line with the given point and slope in point-slope form. Then rewrite the equation in slope-intercept form:

1. \((x_1,y_1) = (2,3)\) and \(m=2\)

2. \((x_1,y_1) = (-1,4)\) and \(m = \frac{1}{2}\)

3. \((x_1,y_1) = (4,0)\) and \(m = 0\)

4. \((x_1,y_1) = (0,-1)\) and \(m = -5\)

Use the following graph to answer questions 5-10

5. Use the graph to find the slope of the blue line (review slope).

6. Find the coordinates of the red dot.

7. Use your answers to Exercises 5 and 6 to write the equation of the blue line in point-slope form. Rewrite the equation in slope-intercept form.

8. Find the coordinates of the green dot.

9. Use your answers to Exercises 5 and 7 to write the equation of the blue line in point-slope form. Rewrite the equation in slope-intercept form.

10. What do you notice about the answers to Exercises 7 and 9? Is this what you would expect to happen?

Algebra Lesson 2.5: Parallel and Perpendicular Lines

Practice Exercises:

Are the following equations parallel, perpendicular, or neither?

1. \(y = 2x+3\) and \(y= 2x + 7\)

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

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

Use the following graph to answer Exercises 4-6

4. What is the slope of the red line? What is the slope of the blue line?

5. Are the red and blue lines parallel, perpendicular, or neither?

6. What is the slope of the green line? Are the red and green lines parallel, perpendicular, or neither?

7. What is the slope of the purple line? Draw a graph containing the purple line and a line perpendicular to it. What is the slope of the line that is perpendicular to the purple line?

Algebra Lesson 2.4: Special Cases when Slope is Zero or Undefined

Practice Problems:

For questions 1-3 refer to the following graph:

1. Is the slope of the green line zero, undefined, or neither?

2. Is the slope of the red line zero, undefined, or neither?

3. Is the slope of the blue line zero, undefined, or neither?

4. What is the slope of the line \(y = 3\)? (hint: remember that the equation of a line is given by \(y=mx+b\) where m is the slope and \(b\) is the \(y\) intercept).

Algebra Lesson 2.3: The Slope-Intercept Form

Practice Exercises:

Identify the slope \(m\) and the \(y\)-intercept \(b\) in the following equations:

1. \(y = 2x + 3\)

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

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

Given the slope \(m\) and the \(y\)-intercept \(b\), write the equation of the line:

4. \(m = 7\), \(b = \frac{1}{3}\)

5. \(m = -0.5\), \(b = -6.7\)

6. \(m = \frac{1}{7}\), \(b = \frac{2}{9}\)

Algebra Lesson 2.2: Slope of a Line

Practice Exercises:

Exercises 1-3 refer to the following graph:

1. What is the slope of the red line?

2. What is the slope of the green line?

3. What is the slope of the blue line?

For the next few problems, you will need to draw your own graphs. (printable graph paper template).

4. Graph any line with a slope of 2

5. Graph any line with a slope of \(-\frac{3}{4}\)

6. Graph any line with a slope of \(\frac{3}{2} \)

Algebra Lesson 3.1: Graphing a Linear Equation by Plotting Points

Practice Exercises:

Graph the given equation of a line by finding the points on the line corresponding to the given \(x\) values, and then drawing the graph of the line through those two points.

     1. \(3y+x = -1\); \(x = -2\) and \(x = 2\)
     2. \(y=2x-1\); \(x=-1\) and \(x=3\)

Solutions video:

Algebra Lesson 2.1: The Equation of a Line

Practice Exercises:

For each given equation, decide whether or not it is the equation of a line:

     1. \(3y+7x=19\)
     2. \(7x-8y=2x\)
     3. \(y + 2x^2 = 11\)
     4. \(x+3y-z = 18\)

Solutions video:

Algebra Lesson 2.5: Plotting Points from a Function

Practice Exercises:

For the given function \(f(x)\), plot the three points \((-1,f(-1))\), \((0,f(0))\),  \((1,f(1)), \) and on a graph.

     1. \(f(x) = 4x-1\)
     2. \(f(x)= -3x+2\)

Solutions video: