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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.

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Section 2.3 Linear Functions and Slopes

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  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)

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