2. UNIT 5 Ms. Andrejko

3. 5.1 NOTES  X-intercept: where the line crosses the x-axis  Written as (x,0)  Y-intercept: where the line crosses the y-axis  Written as (0,y) X-intercept y-intercept

4. 5.1 Notes  To graph the line of an equation using the intercepts:  1. Find the x-intercept of a given equation by substituting a 0 for y, and solving for x  2. Find the y-intercept of a given equation by substituting 0 for x and then solving for y (x, 0) (0, y)

5. 5.1 Examples  1. Find the x & y intercepts

6. 5.1 Examples  2. Graph 3x+2y=6  3. Graph y= 2/3x +5

7. 5.1 Examples  4. The ticket price for students (x) to attend a school basketball game is $3 and adults (y) pay $5. The sports program took in $510.  Equation:  X-intercept:  Y-intercept:  X-intercept represents:

8. Bellwork 1.2. Graph: 3x - 4y = 12 X-intercept:3. Graph: 5x + 2y = -10 Y-intercept:

9. 5.2 NOTES SLOPE, X&Y INTERCEPTS 1. Slope (m) 2. To find the slope of a line: 1. Identify 2 points on the line with x&y values that are not fractions 2. Draw a slope triangle from the lower point to the higher point 1. Useof the triangle to write the slope. Rise is the height. Run is the length

10. 5.2 NOTES 4. Determine if the slope is negative or positive by the direction of the line. * line going up from L  R is POSITIVE * line going down from L  R is NEGATIVE 5. Reduce fraction if possible positivenegative undefined zero

11. 5.2 Examples Slope: X-int: Y-int: Slope: X-int: Y-int: 1.2.

12. 5.2 Examples Slope: X-int: Y-int: Slope: X-int: (-3,0) Y-int: (0,2) 3.

13. 5.2 Examples Slope: - ½ X-int: Y-int: (0,2)

14. Bellwork slope is: _______ x-intercept is: ______ y-intercept is: ______ slope is: _______ x-intercept is: ______ y-intercept is: ______ Slope: 2 Y-intercept (0, -6) X-intercept (, )

15. 5.3 NOTES  Steps: 1. Graph the y-intercept on the y-axis (1 st point) 2. If the slope (m) is not a fraction, make it a fraction by putting a 1 in the denominator ex: 2 = 2/1 y=mx+b Y-intercept slope

16. 5.3 NOTES 3. From the point on the y-intercept, go up the # in the numerator (rise), and go left or right the number in the denominator (run) *If the slope is positive, go right * If the slope is negative, go left 4. Connect the two points. Make sure your lines have arrows!

17. 5.3 Examples 1. y=2x-12. y=-2x 3. y= ½ x+34. y= 2/3 x+5

18. 5.3 Examples 5. y= 0x+16 (a) 7 (b)8 (c)

19. Bellwork 1.2. 3.4. Y= ½ x +3 Y= -2x - 4 Equation:

20. 5.4 Notes Goal: isolate the y-term on the right side of the equal sign. Then, identify m and b & graph the line. Steps: 1. Move the x-term to the right side of the = sign by adding its opposite 2. If there’s a coefficient of “y” ( a # in front of y), divide it by every term on both sides of the = sign to completely isolate the “y”

21. 5.4 Examples  Solve for y: a. x+y = 0b. -2x -3y = 6

22. 5.4 Examples  Solve for y & GRAPH: a. 2x + ½ y = -2b. -4x – 6y = 12

23. Bellwork- Solve for y & graph -x + y = 5 2x + y = -4 –x + y = -1 x y x y x y

24. 5.5 Notes  Connecting graphing a line using table of values/intercepts/slopes To graph the line of an equation using a table of values: 1. Choose 3 x-values, usually 0,1,2 or -1,0,1. Any 3 values will work, just make sure the points fit the graph. 2. Find the corresponding y-values by plugging each x- value into the equation where the “x” is, one at a time.

25. 5.5 Notes 3. Calculate the right side of the equation. Whatever your answer is, put it in the y-value spot. This is a point on the line you will graph (x,y) 4. Graph the point 5. Follow steps 1-4 for all 3 x-values 6. Graph all 3 points & connect them to form a straight line

26. 5.5 Examples

27. d.Describe the difference in the lines of y = 2x and y = -2x graphed above. e.What part of the equation, do you think, effects the direction of the line? f.In “h” above, where does the line touch the y-axis? g. Where do you think the line of y = x – 4 will touch the y-axis?

28. 5.5 Examples

29. When graphing an equation with a fraction, choose the negative and positive of the denominator (bottom) of the fraction and zero for the 3 values of “x”. This way none of the “y” values will end up fractions, which are much harder to graph.

30. Bellwork Y = x - 5 Y = ½ x +2Y = 3x - 1

31. 5.6 Notes  Graphing Horizontal & Vertical Lines 1. Equations w/ only ONE variable graph either horizontal or vertical lines 2. An equation with only a “y”, like y=1, graphs a horizontal line 3. An equation with only an “x”, like x=2, graphs a vertical line y=1, is the same as y=0x+1, so the slope (m) is zero & y-intercept is 1

32. 5.6 Notes x=1 cannot be written into y=mx+b because it has no “y”. This equation has no slope & no y-intercept 4. Slope of horizontal line is 0 5. Slope of vertical line is undefined

33. 5.6 Examples 1. y=-22. x=33. 2y=4

34. Bellwork – Graph the lines: 1. x=-52. 3x = 153. -4y=16