1. Slope and Equations of Lines

2. Reviewing types of slope Remember, there are four types of slope: PositiveNegative No slope Undefined slope

3. The slope of a line  The slope of a nonvertical line passing thru the points (x 1,y 1 ) (x 2,y 2 ) :

4. Find the slope of a line passing thru (-3,5) & (2,1)

5. W/out graphing, tell whether the line thru the points is positive, negative, horizontal, or vertical.  1) (3,-4), (1,-6)  2) (2,-1), (2,5) Undefined: The line is vertical m>0, positive slope

6. What is the slope of the line? The constant, b = 3 is the y-intercept. The coefficient, m = -2 is the slope.

7. Fill in the Blank  Parallel Lines have the _______ slope.  Perpendicular Lines have slopes that are _________ __________.

8. Ex: y = 3x - 6 A. y = 2x + 1 B. y = 3x + 4 C. y = -3x + 6 D. y = Which equation is parallel? Which equation is perpendicular?

9. Ex: 4x – 8y = -16 A. y = 2x + 4 B. y = -2x - 1 C. y = -½x - 3 D. y = Which equation is parallel? Which equation is perpendicular?

10. Ex : Tell whether the lines are װ, ┴, or neither  L 1 : thru (-3,3) & (3,-1)  L 2 : thru (-2,-3) & (2,3) Negative reciprocals Of each other : They are ┴.

11. Equation of a Line  What is slope-intercept form?

12. Find the slope of the line y = 2x - 4. Slope-Intercept Form y = 2x - 4 -8-6-4 -2 2 42 68 4 6 -4 -6 -8 -2 8 The y-intercept is -4.

13. up 2 right 1 up 2 right 1

14. Example: Graph 3x + 4y = –12 Step 1: Put equation in slope – intercept form

15. Example  Write the equation of the line with slope = -2 and passing through the point (3, -5).  Substitute m and substitute into the Slope Intercept Form.  Y=-2x+b  -5=-2(3)+b  1=b  Y=-2x+1

16. Ex : Write the equation of the line with m=3 and through the point (2,-3)  Y=mx+b  Y=3x+b  -3=3(2)+b  -9=b

17. Write the Equation for the line:  Through (-2,1) and parallel to y=-3x+1  Plug the point (-2,1) into the equation y=mx+b 1=m(-2)+b  If it is parallel, then they have the same slope! So m=-3, therefore, 1 = (-3)(-2)+b 1 = 6+b -6 -6 -5 =b  Write the equation of the new line: Y=-3x-5

18. Write the equation of the line:  Perpendicular to y=3x-4 that passes through the point (3,2).  2=m(3)+b  Slope is the neg. reciprocal so m=-1/3.  2=-(1/3)(3)+b  2=-1+b  3=bEquation: y=-1/3x+3

19. Parallel to the line 2x+y=6 thru (3,4).

20. Perpendicular to the line -3x+ y=4 thru (6,4)