Unit 5: Moving Straight Ahead Name: Key

Transcription

1 Unit 5: Moving Straight Ahead Name: Key 1.1: Finding and Using Rates 1.: Tables, Graphs and Equations 1.3: Using Linear Relationships Independent Variable: One of the two variables in a relationship. Its value determines the value of the other variable called the dependent variable. If you organize a bike tour, for example, the number of people who register to go (independent variable) determines the cost for renting bikes (dependent variable). Dependent Variable: One of the two variables in a relationship. Its value depends upon or is determined by the other variable called the independent variable. For example, the distance you travel on a car trip (dependent variable) depends on how long you drive (independent variable).

2 Problem 1.3: A1) Independent Variable: Distance (x-axis) Dependent Variable: Money (y-axis) A) Graph all 3 pledges on same axes: A3) Equations for each plan: Gilberto Alana Leanne Leanne: y = 10 Gilberto: y = x (Proportional) Alana: y = x : Recognizing Linear Relationships Straight line graph * To be a proportional relationship, the graph must start at 0 and go up at a constant rate

3 .1/.: Finding the Point of Intersection Using Tables Graphs and Equations.3: Comparing Relationships x-intercept: The point where a graph crosses the x-axis. In the graph, the coordinates of the x- intercept are ( 4, 0). y-intercept: The point where the graph crosses the y-axis. In a linear equation of the form y=mx+b, the y-intercept is the constant, b. In the graph, the y-intercept is (0, ) or.

4 Independent Variable: # of T-shirts Dependent Variable: Cost Mighty Tee: C = 49 + n No-Shrink Tee: C = 4.5n y-intercept & what it 49- Starting $ 0- Starting $ represents Coefficient of n & 1- Cost per shirt 4.5- Cost per shirt what it represents Cost for 1 T-shirts C = = $61 C = = $54 Cost for 0 T-shirts C = = $69 C = = $90 How many T-shirts for $10? 10 = 49 + n n = 71 t-shirts 10 = 4.5n n = 6.6 = 6 shirts A4) For what number of T-shirts is the cost of the companies equal? What is the cost? 49 + n = 4.5n -n -n 49 = 3.5n n = 14 shirts C= = $63 14 = n

5 .4: Connecting Tables, Graphs and Equations Ex: Match the following equations, tables and graphs: x y x y x y y = -3x 1 y = 3 x + 4 y = 4 3.1: Solving Equations Using Tables and Graphs 3.: Exploring Equality

6 3.3: Writing Equations Equivalent Expressions: Expressions that represent the same quantity. For example, + 5, 3 + 4, and 7 are equivalent expressions. You can apply the Distributive Property to (x + 3) to write the equivalent expression x + 6. You can apply the Commutative Property to x + 6 to write the equivalent expression 6 + x. Properties of Equality: For all real numbers a, b, and c: Addition: If a = b, then a + c = b + c. Subtraction: If a = b, then a - c = b - c. Multiplication: If a = b, then a c = b c. Division: If a = b and c 0, then ac = bc. Problem 3.3 B: Solve the equation. Check your answer. 1) 30 = 6 + 4x ) 7x = 5 + 5x Check Step = (6) -5x -5x 30 = = 4x x = 5 30 = Check Step 7 (.5) = (.5) 17.5 = = = x x =.5 3) 7x + = 1 + 5x 4) (x + 4) = 16 Check Step -5x -5x x + 8 = 16 7 (5) + = (5) x + = = = 37 x = 8 Check Step (4 + 4) = 16 (8) = = 16 x = 10 x = 4 x = 5

7 4.1: Using Rise and Run/ 4.: Finding the Slope of a Line Slope: The number that expresses the steepness of a line. The slope of a line is the same as the constant rate of change between the two variables. Rise Run Ex: a) Find the slope of the line Rise = Run Change in y axis (vertical) = 4 3 = 1 Change in x axis (horizontal) 4 b) Write the equation for the line y = mx + b m is slope ( 1 ) b is y intercept (where it crosses y-axis ()) Equation: y = 1 x + 1

8 4.3: Exploring Patterns with Lines 4.4: Writing Equations for Linear Relationships Ex: Does the table represent a linear relationship? If so, write an equation for that relationship? slope (rate) = 8 = 8 = 0 5 = 4 Change Time (hr) Distance (mi) Change Since the distance/time goes up at a constant rate of 4 mi per hour, then this is a linear relationship. The starting amount (y-intercept) if you count back 4 miles to 0 hours would be a starting distance of 5 miles. Equation: d = 4t + 5 (if d is distance and t is time)