February 16 2016
- 1. Today: Review for Thursday's Test This Week's Khan Academy Topics New Concept: The Slope of a Line CW 3.5 Questions Answered (Due Tomorrow) Progress Reports Thursday February 16, 2016
- 2. But first...the final results from the thrilling world of Cricket...
- 4. 1st Coordinate Plane Test: Thursday, Feb. 18; The Test will include the following: Functions, Domain, Range Ordered Pair Solutions Standard Form of a Line/Intercepts Slope of a Line For today, you need: Grade trackers, Notebook, graph paper, calculator Work the problems out. A wrong answer is far better than no answer..
- 5. Find Intercepts from a Linear Equation 2/21/16 Topic Due Date Domain & Range from Graph 2/21/16 Interpreting Graphs of Linear & Non-Linear Functions 2/21/16
- 6. W A R M ● U P Graph Paper Out ● ●
- 7. Domain & Range from Graph -3 9 -3 6 Is the graph a function? Is the graph a linear function?
- 8. Domain & Range from Graph -6 6 -8 9 Is the graph a function? Is the graph a linear function?
- 9. Domain & Range from Graph Is the graph a function? Is the graph a linear function? -2 7 0 4
- 10. 1. The x values in a relation are called the: 2. The range of this relation { (-2,1); (-4,1); (2,5); (-2,3); (4,8); } is: a) {-2,1,2,-2,4} b) {1,3,5,3,8} c) {1,1,5,3,8} d) {-2,1,2,-4,8} e) none 3. Given y = -2x – 3, the f (-5) is: 4. What are the x and y intercepts for: 2x – 6 = y 5. Which ordered pair is not a solution to: y = 4x - 10 a) -13 b) 0 c) -3 d) 7 e) none a) (0,4) b) (3,0) c) (3,-6) d) (-3,6) e) none 5 Question Test Review: a) (1,-6) b) (0,-10) c) (-1,-6) d) (2,-2) e) none Number your paper 1-5; do not say the answer out loud... a) domain b) range c) ordered pair d) output e) none
- 11. Graph the equation with at least 3 points: 3y = 2x - 6 Can you simplify an equation, say, 4x - 6y = 12 and still get the same line? Where/How to Start? - 2x +3y = -6; 2x - 3y = 6 2x - 3(0) = 6 x = 3 ● 2(0) - 3y = 6 y = -2 ● ● Use the slope of the line to find one more point. What is the y coordinate when x is 150? y = 98 ...Find the intercepts + + - - Graph paper out, try to work the problem completely!
- 12. y is 4 more than the product of 7 and x; x = 3 Write a function rule that represents each sentence. Then find the value of y for the given value of x. You got the answer correct. That's good, but what does it mean? What do those two numbers represent? y is 11 less than 𝟏 𝟑 of x; x = 72 Write the following function rule in function notation. Again, find the value of the function at the given x. f(x) = 𝟏 𝟑 (72) - 11 f(x) = 13 y = 7(3) + 4; y = 25 Warm-Up Find any other point on this same line.
- 13. 2. Find the range values of the function for the given domain. f(x) = -3x + 2 ; {-5, -2, 6} Steps 1. Sub in each domain value one @ a time. 2. Solve for y in each equation 3. List y values in braces. The range values of the function f(x) = -2x + 3, with a domain of {-5, -2, 6} are..... {17, 8, -16} Test Review What are three of the coordinates of this line? (-5, 17), (-2, 8), (6, -16)
- 14. Test Review
- 15. Test Review
- 16. From the graph below, which equation contains point B? Test Review
- 19. x y x2 – x1 y2 – y1 change in y change in x The slope of the line passing through the two points (x1, y1) and (x2, y2) is given by the formula (x1, y1) (x2, y2) x2 – x1 The rise is the difference of the y-values of two points on a line. The run is the difference in the x-values of two points on a line. The constant rate of change of a straight line is called the slope. The Slope of a Line: Slope is usually represented by the letter m (from the French, monter, which means “to go up”). Straight Lines (linear functions) are straight because the slope never changes!!
- 20. (3, 2) (–1, –2) Then count horizontally to a second point to find the run. Count vertically from any one point on the line to find the rise. Finding the Slope of a Line slope = 𝟒 𝟒 = 1 The slope of the line is 1. It does not matter which ordered pair you start with. slope = −𝟒 −𝟒 = 1 4 4
- 21. (5, 4) Then count horizontally to a second point to find the run. Count vertically from any one point on the line to find the rise. slope = 𝟐 𝟒 = 𝟏 𝟐 The slope of the line is 𝟏 𝟐 slope = −𝟐 −𝟒 = 𝟏 𝟐 Find the slope of the line: It does not matter which y you begin from. (1, 2) The Slope of a Line The slope of a line is the ratio of rise to run for any two points on the line. change in y change in x Rise Run =
- 22. Find the slope of the line passing through the points (2, 3) & (4, 5). The x1 and y1 must come from the same ordered pair. y2 – y1 x2 – x1 m = 5 – 3 4 – 2 = = 2 2 = 1 2 2(2, 3) (4, 5) x y The Slope of a Line Name one other ordered pair on this line.
- 23. The Slope of a Line What is the slope of this, and all horizontal lines? Don't guess, just plug the numbers in... All horizontal lines have a slope of zero.
- 24. The Slope of a Line What is the slope of this, and all vertical lines? All vertical lines have a slope that is undefined because... a denominator cannot be zero.
- 25. m = 0 m = 2 m is undefined m = 1 2 m = - 1 4 y2 – y1 x2 – x1 m = The Slope of a Line
- 26. The Slope of a Line
- 27. What is the slope of the line? The Slope of a Line
- 28. What is the equation of this line? The point here, is called the.... y-intercept. We know the slope, and the y-intercept, so... y = 𝟐 𝟑 x - 2 What is the slope of this line? The Slope of a Line