1 / 19

Quick Review:

Slope is… Steepness of a line , m , rise , change in y , common difference run change in x Positive Slope: Negative Slope: Zero Slope: Undefined Slope:. Quick Review:. Chapter 12-3. Slope and Intercepts.

wilmaallen
Download Presentation

Quick Review:

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. Slope is… Steepness of a line, m, rise, change in y, common difference runchange in x Positive Slope: Negative Slope: Zero Slope: Undefined Slope: Quick Review:

  2. Chapter 12-3 Slope and Intercepts

  3. How to graph a linear equation (one that forms a straight line and also has a common difference – constant slope) using intercepts. What slope-intercept form is and how to put any linear equation into slope-intercept form. Topics to learn today:

  4. There are 2 different ways to graph a linear equation: • Finding the x and y intercepts and plotting them on a graph (today). • Using the slope and y-intercept (in slope-intercept form) to graph 2 points on a coordinate plane (Wednesday).

  5. Steps to graph a linear equation using intercepts: Find the x-intercept (y=0) Find the y-intercept (x=0) Plot the points Connect the points with a line

  6. **The x-intercept of a line is the value of x where the line crosses the x-axis (where y = 0). x-axis y-axis X-intercept:

  7. **The y-intercept of a line is the value of y where the line crosses the y-axis (where x = 0). x-axis y-axis y-intercept:

  8. 8x = 24 8 8 Graphing linear equations: Graph the line 8x – 6y = 24 using the intercepts. 1. Find the x-intercept (y = 0). 8x – 6y = 24 8x – 6(0) = 24 8x = 24 The ordered pair for the x-intercept is (3,0). x = 3 The x-intercept is 3.

  9. –6y –6 = 24 –6 Graphing linear equations: 2. Find the y-intercept (x = 0). 8x – 6y = 24 8(0) – 6y = 24 –6y = 24 y = –4 The ordered pair for the y-intercept is (0,-4). The y-intercept is –4.

  10. The graph of 8x – 6y = 24 is the line that crosses the x-axis at the point (3, 0) and the y-axis at the point (0, –4).

  11. y = mx + b Slope y-intercept **Slope-intercept form: y= mx+ b mis the slope and bis the y-intercept.

  12. Slope-intercept form is how you need an equation to be so that you can EASILY graph it. Standard form is another way of seeing a linear equation, but you can’t graph it – you would have to put it into slope-intercept form.

  13. Helpful Hint The form Ax + By = C is called the Standard Formof a Linear Equation. **Remember… slope-intercept form is y= mx+ b

  14. To put any linear equation into slope-intercept form, you have to use inverse operations to solve for y.

  15. Let’s put this equation in slope-intercept form: 5y = x 5 3 3 5 5 y = x + 0 3 m = 5 3 The slope of the line 5y = 3x is , and the y-intercept is 0. 5 5y = 3x 5y = 3x Divide both sides by 5 to solve for y. The equation is in slope-intercept form. b = 0

  16. You always have to have a y, m, x, and b. This means that if an equation says y=mx, you assume that b is 0 (and add 0). y = mx + 0

  17. 3y 3 4 –4x 3 3 4 9 3 = + 3 4 y =- x + 3 m =- 3 The slope of the line 4x+ 3y = 9 is – , and the y-intercept is 3. Change from standard form to slope-intercept form: 4x + 3y = 9 4x + 3y = 9 –4x–4x Subtract 4x from both sides. 3y = 9 – 4x Rewrite to match slope-intercept form. 3y = –4x + 9 Divide both sides by 3. The equation is in slope-intercept form. b= 3

  18. -5x – 9x = 4y – 4 -6y – 2x = 8 7y – 7x = -4 1y – 3x = 4

  19. A video club charges $8 to join, and $1.25 for each DVD that is rented. The linear equation y = 1.25x + 8 represents the amount of money y spent after renting x DVDs. Graph the equation by first identifying the slope and y-intercept. The equation is in slope-intercept form. y = 1.25x + 8 m =1.25 b = 8

More Related