1 / 42

Section 2.3 Linear Functions and Slopes

Section 2.3 Linear Functions and Slopes. The Slope of a Line. Example. Find the slope of the line passing through the pair of points. (5,-2) and (-1,7). The Point-Slope Form of the Equation of a Line. x 1. y 1. Solving in both forms.

jermaine-roth
Download Presentation

Section 2.3 Linear Functions and Slopes

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 2.3Linear Functions and Slopes

  2. The Slope of a Line

  3. Example Find the slope of the line passing through the pair of points. (5,-2) and (-1,7)

  4. The Point-Slope Form of the Equation of a Line

  5. x1 y1 Solving in both forms • A.Write the equation in point slope form of the line with slope 4 that passes through the point (4,-3). B.Then solve the equation for y (slope intercept form) • y-y1 = m(x-x1) y-(-3) = 4(x-4) Substituting the values into the euation y+3 = 4(x-4) This is Point Slope Form. Apply the distributive property for the parentheses. This will give us the slope intercept form. (The equation is solved for y.) -3 -3 y= 4(x-4)-3 y= 4x-16-3 Y=4x-19

  6. Example Write the point slope form of the equation of the line with slope of -4 that passes through (2,5). Then solve for y.

  7. If you are given two points and you need to write an equation in point-slope form, then you can use either point for (x1,y1).

  8. Example Write the point slope form of the equation of the line that passes through (2,5) and (-1,0). Then solve for y.

  9. The Slope-Intercept Form of the Equation of a Line

  10. Two forms for Equations of Lines

  11. Graph the linear equation y= 2/3x+4 First: Plot the y-intercept of 4 Rise by 2 units Run ( go to the right) by 3 units. Plot the second point (3, 6) Connect the two points with a straight edge or ruler. (3,6) (0,4)

  12. Example Graph the linear equation y= -3x+5

  13. Example

  14. Equations of Horizontal and Vertical Lines

  15. Example Graph x=4. Graph y=-2

  16. The General Form of the Equation of a Line

  17. Y intercept slope

  18. Example Find the slope and the y intercept of the line whose equation is 2x+5y-10=0.

  19. Using Intercepts to Graph Ax + By + C = 0

  20. Find x and y intercepts to graph a line 6x-2y=12 0 0 6x-2(0)=12 6(0)-2y=12 6x=12 -2y=12 X=2 Y=-6 (2,0) (0,-6)

  21. Example Find the x and y intercepts then graph using those points. X-4y-8=0

  22. Summary

  23. Applications

  24. Example

  25. Graphing Calculator-Linear Regression More on the next slide.

  26. Graphing Calculator-Linear Regression continued

  27. Find the equation of the line in slope-intercept form for a line that passes through (0,-4) and has a slope of -2. (a) (b) (c) (d)

  28. Find the equation of the line in slope-intercept form of the line that passes through (-3,-2) and (0,-2). (a) (b) (c) (d)

  29. What is the slope of the line 3x - 7y – 4 = 0. (a) (b) (c) (d)

More Related