1 / 28

Graphing Linear Equations Using Intercepts: Examples and Checkpoints

Learn how to graph linear equations by identifying x- and y-intercepts, finding checkpoints, and drawing the line through these points. Examples provided.

marcussmith
Download Presentation

Graphing Linear Equations Using Intercepts: Examples and Checkpoints

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Section 3.2 • Graphing Linear Equations • Using Intercepts

  2. Objective 1 • Use a graph to identify intercepts.

  3. Linear Functions • straight lines when graphed, as long as A and B are not both zero. • Such an equation is called the standard form of the equation of the line. • To graph equations of this form, two very important points are used – the intercepts.

  4. x-intercept An x-intercept of a graph is the x-coordinate of a point where the graph intersects the x-axis. The y-coordinate corresponding to an x-intercept is always zero. The graph of crosses the x-axis at (2, 0) and that point is the x-intercept.

  5. y-intercept The y-intercept of a graph is the y-coordinate of a point where the graph intersects the y-axis. The x-coordinate corresponding to a y-intercept is always zero. The graph of crosses the y-axis at (0, 4) and that point is the y-intercept.

  6. Objective 1: Examples 1a.Identify the x- and y-intercepts: The graph crosses the x-axis at (3,0). Thus, the x-intercept is 3. The graph crosses the y-axis at (0,5). Thus, the y-intercept is 5.

  7. Objective 1: Examples 1b.Identify the x- and y- intercepts: The graph crosses the x-axis at (0,0). Thus, the x-intercept is 0. The graph crosses the y-axis at (0,0). Thus, the y-intercept is 0.

  8. Objective 2 • Graph a linear equation in two variables • using intercepts.

  9. x- and y-Intercepts

  10. Example Graph the equation using intercepts. Find the x-intercept. Let y 0 and then solve for x. Replace y with 0. Multiply and simplify. Divide by 2. The x-intercept is 6, so the line passes through (6,0).

  11. Example (cont) Find the y-intercept. Let x 0 and then solve for y. Replace xwith 0. Multiply and simplify. Divide by 4. The y-intercept is 3, so the line passes through (0,3).

  12. Example (cont) Find a checkpoint, a third ordered-pair solution. For our checkpoint, we will let x1 (because x1 is not the x-intercept) and find the corresponding value for y. Replace x with 1. Multiply. Add 2 to both sides. Divide by 4 and simplify. The checkpoint is the ordered pair (1, 3.5).

  13. Example (cont) Graph the equation by drawing a linethrough points. The three points in the figure below lie along same line. Drawing a line through the three points results in the graph of

  14. Example • 1. Find the x-intercept. Let y0 and solve for x. • The x-intercept is 4. The line passes through (4, 0). • 2. Find the y-intercept. Let x0 and solve for y. • The y-intercept is 3. The line passes through (0, 3).

  15. Example (cont) • 3. Find a checkpoint, a third ordered-pairsolution. Let x2. • A checkpoint is the ordered pair (2, 1.5).

  16. Example (cont) • 4. Find a equation by drawing a line through the intercepts and checkpoint.

  17. Objective 2: Examples 2a.Find the x-intercept of the graph of To find the x-intercept, let y 0 and solve for x. The x-intercept is 3.

  18. Objective 2: Examples 2b. Find the y-intercept of the graph of To find the y-intercept, let x0 and solve for y. The y-intercept is 4.

  19. Objective 2: Examples • Find the x-intercept. Let y0 and solve for x. • The x-intercept is 3. • Find the y-intercept. Let x 0 and solve for y. • The y-intercept is 2.

  20. Objective 2: Examples(cont) • Find a checkpoint. For example, let x 1 and solve for y.

  21. Objective 2: Examples Because the constant on the right is 0, the graph passes through the origin. The x- and y-intercepts are both 0. Thus we will need to find two more points. Let y1 and solve for x.

  22. Objective 2: Examples(cont) • Let y 1 and solve for x. • Use these three solutions of (0,0), (3,1), and ( 3,1).

  23. Objective 3 • Graph horizontal or vertical lines.

  24. Horizontal and Vertical Lines

  25. Example • Graph the linear equation: y -4 • All ordered pairs that are solutions of y-4 have a value of y that is always -4. Any value can be used for x. Let’s select three of the possible values for x: -3, 1, 6. (1, -4) (-3, -4) (6,-4)

  26. Example • Graph the linear equation: x 5 • All ordered pairs that are solutions of x 5 have a value of x that is always 5. Any value can be used for y. Let’s select three of the possible values for y: -3, 1, 5. (5,5) (5,1) (5,-3)

  27. Objective 3: Examples • 3a. Graph: y 3 • As demonstrated in the table below, all ordered pairs that are solutions of y 3have a value of ythat is always 3. • Thus, the line is horizontal.

  28. Example (cont) • 3b. Graph: x -2 • As demonstrated in the table below, all ordered pairs that are solutions of x -2 have a value of xthat is always -2. • Thus the line is vertical.

More Related