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Exit Level

Exit Level. TAKS Preparation Unit Objective 3. Interpreting Linear Functions. Functions can be represented in different ways: y = 2x + 3 means the same thing as f(x) = 2x + 3 Linear Functions must have a slope (rate of change) and a y intercept (initial value). In a function…

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Exit Level

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  1. Exit Level TAKS Preparation Unit Objective 3

  2. Interpreting Linear Functions Functions can be represented in different ways: y = 2x + 3 means the same thing as f(x) = 2x + 3 Linear Functions must have a slope (rate of change) and a y intercept (initial value). In a function… • the slope is the constant (number) next to the variable • the y intercept is the constant (number) by itself 3, A.05A

  3. Interpreting Linear Functions, cont… 425 50 • Example: Identify the situation that best represents the amount f(n) = 425 + 50n. Slope (rate of change) = Y intercept(initial value) = Find an answer that has: 425 as a non-changing value and 50 as a recurring charge every month, every year, etc… Something like Joe has $425 in his savings account and he adds $50 every month. 3, A.05A

  4. Converting Tables to Equations • When given a table of values, USE STAT! • Example:What equation describes the relationship between the total cost, c, and the number of books, b? Answer: c = 5x + 25 3, A.05C

  5. Converting Graphs to Equations • Make a table of values • Then, use STAT! • Example:Which linear function describes the graph shown below? -2 5 0 4 2 3 4 2 Answer: y = -.5x + 4 3, A.05C

  6. Converting Equation to Graph • Graph the function in y = • Example: Which graph best describes the function y = -3.25x + 4? Find an answer that has the same y intercept and x intercept as the calculator graph. 3, A.05C

  7. Equations that are in Standard Form • Sometimes your equations won’t be in y = mx + b form. • They will be in standard form: Ax + By = C • You must convert them to use the calculator! Example: 3x + 2y = 12 Step 1:Move the x -3x -3x 2y = -3x + 12 Step 2:Divide everything by the number in front of y 2 2 2 3, A.05C

  8. Slope and Rate of Change (m) • Slope and rate of change are the same thing! • They both indicate the steepness of a line. • Three ways to find the slope of a line: By Formula: By Counting: By Looking: You must have 2 points on a line You must have a graph You must have an equation 3, A.06A

  9. Slope and Rate of Change (m), cont… • By Formula: • Find two points on the graph (they won’t be given to you) (0, 4) and (2, 3) 3, A.06A

  10. Slope and Rate of Change (m), cont… • By Counting • Find two points on the graph Down 2 Right 4 3, A.06A

  11. Slope and Rate of Change (m), cont… • By Looking • The equation won’t be in y = mx + b form • You’ll have to change it • If in Standard Form use Process on Slide 7 • If in some other form, you’ll have to work it out… Example: What is the rate of change of the function 4y = -2(x – 24)? Try to get rid of any parentheses and get the y by itself (isolated). 4y = -2x + 48 4 4 4 3, A.06A

  12. Slope and Rate of Change (m), cont… • Special Cases • Horizontal lines line y = 4 Have slope of zero, m = 0 • Vertical lines like x = 4 Have slope that is undefined 3, A.06A

  13. m and b in a Linear Function • Changes to m, the slope, of a line effect its steepness y = 1/3x + 0 y = 1x + 0 • Changes to b, the y intercept, of a line effect its vertical position (up or down) y = 3x + 0 y = 1x + 3 y = 1x + 0 y = 1x - 4 3, A.06C

  14. m and b in a Linear Function, cont… • Parallel Lines have equal slope (m) y = ¼ x – 3 and y = ¼ x + 6 • Perpendicular Lines have opposite reciprocal slope (m) y = ¼ x – 5 and y = -4x + 15 • Lines with the same y intercept will have the same number for b y = ¾ x – 9 and y = 5x – 9 3, A.06C

  15. Linear Equations from Points • Make a table • USE STAT • Example:Which equation represents the line that passes through the points (3, -1) and (-3, -3)? Answer: 3, A.06D

  16. Intercepts of Lines • To find the intercepts from a graph… just look! • The x intercept is where a line crosses the x axis • The y intercept is where a line crosses the y axis (0, 2) (4, 0) 3, A.06E

  17. Intercepts of Lines, cont… • To find intercepts from equations, use your calculator to graph them • Example:Find the x and y intercepts of 4x – 3y = 12. -4x -4x -3y = -4x + 12 -3 -3 -3 x intercept: (3, 0) y intercept: (0, -4) 3, A.06E

  18. Direct Variation • Set up a proportion! • Make sure that similar numbers appear in the same location in the proportion • Example:If y varies directly with x and y is 16 when x is 5 what is the value of x when y = 8? 16x = 5(8) 16x = 40 16 16 x = 2.5 3, A.06F

  19. Direct Variation, cont… • To find the constant of variation use a linear function (y = kx) and find the slope • The slope, m, is the same thing as k • Example:If y varies directly with x and y = 6 when x = 2, what is the constant of variation? The equation for this situation would be y = 3x y = kx 3 = k 6 = k(2) 2 2 3, A.06F

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