Transcript Document
What am I Learning Today? Graphing on a Coordinate Plane How will I show that I learned it? Locate and graph ordered pairs in Quadrant I Vocabulary • Coordinate plane: Formed by two number lines in a plane that intersect at right angles. • Axes: Two number lines in a coordinate plane. X-axis is horizontal and y-axis is vertical. • Ordered pairs: Gives the location of a point on a coordinate plane. • Coordinate: The numbers in an ordered pair. Questions How is an ordered pair written? What does an ordered pair tell you? Answers (x, y) The first number tells how far to move right (positive) from the origin along the xaxis. The second number tells how far to move up (positive) from the origin along the yaxis. Where is the origin located? (0,0) Graphing Ordered Pairs Graph and label each point on a coordinate grid. A. L (3, 5) Start at (0, 0). Move right 3 units. Move up 5 units. 6 5 L 4 3 B. M (4, 0) Start at (0, 0). Move right 4 units. Move up 0 units. 2 1 0 M 1 2 3 4 5 6 Graphing Ordered Pairs Graph and label each point on a coordinate grid. A. T (2, 6) Start at (0, 0). Move right 2 units. Move up 6 units. B. V (5, 0) Start at (0, 0). Move right 5 units. Move up 0 units. T 6 5 4 3 2 1 0 V 1 2 3 4 5 6 Try These Give the ordered pair for each point. 1. A (4, 6) 2. B (6, 1) 3. C (1, 4) 4. D G F (2, 1) Graph and label each point on a coordinate grid. 5. F(7, 2) 6. G(1, 7) Practice http://www.thatquiz.org/tq-7/?-jc8-l5-n35-p2kc0 What am I Learning Today? Patterns, Tables, and Functions How will I show that I learned it? Analyze and describe patterns arising from mathematical rules, tables and graphs Identify an equation based on a table’s pattern and find the missing values Represent an equation using ordered pairs and translate onto a graph How do you solve with a Table? First, start with an equation. y = 3x Next, create a table INPUT (X) OUTPUT (Y) How do you solve with a Table? y = 3x Put numbers into the input side of the table. We are going to INPUT (x value) each number into the equation above to determine what the OUTPUT (y value) will be. INPUT (X) What is the OUTPUT (y value) for the table? OUTPUT (Y) How do you solve with a Table? y = 7x Put numbers into the input side of the table. We are going to INPUT (x value) each number into the equation above to determine what the OUTPUT (y value) will be. INPUT (X) What is the OUTPUT (y value) for the table? OUTPUT (Y) How do you solve with a Table? y=½x Put numbers into the input side of the table. We are going to INPUT (x value) each number into the equation above to determine what the OUTPUT (y value) will be. INPUT (X) What is the OUTPUT (y value) for the table? OUTPUT (Y) What am I Learning Today? Substitution How will I show that I learned it? Plug in numbers for letters. Questions Answers When you exchange a letter (variable) in an equation What is substitution? for a number and then solve. What kind of equation can we use? y = 6x Did you notice that we are using an x and a y variable? That is because we are going to use the x and the y numbers to graph them. Questions How do you solve a substitution problem? Answers Using y = 6x, what is the value of x if y = 42. Substitute 42 in for the y. It will look like. 42 = 6x That’s a one step equation and we know how to solve that. 42 = 6x 6 6 7=x Now, you practice. Using y = 8x, what is the value of x if y = 56. y = 8x 56 = 8x 8 8 7=x DID YOU GET IT RIGHT? Now you practice. Using y = 3x, what is the value of x if y = 24. y = 3x 24 = 3x 3 3 X=8 DID YOU GET IT RIGHT? Now you practice. Using y = 9x, what is the value of x if y = 108. y = 9x 108= 9x 9 9 12 = x DID YOU GET IT RIGHT? What am I Learning Today? Direct Variation How will I show that I learned it? Recognize direct variation and describe this proportional relationship using an equation Graph proportional relationships Questions Answers What is direct An equation where as 1 variable increases, the other variable increases at the same rate. variation? The two quantities always have equivalent ratios. (Like equivalent fractions) In what 3 ways can direct variation be represented? Table, equation, and graph What does direct variation look like on a graph? A straight line through the point of origin (0,0) Why do the direct variation equations have two variables? Since direct variations can be graphed, there to be an x value and a y value for the equation so we can graph it. Determine whether the values in the table represent a direct variation. If so, write a direct variation equation for the variation. If not, explain. y x y -1 0 -4 0 1 4 2 2.5 8 10 x y 4x Direct-Variation Equation Direct Variation Determine whether the values in the table represent a direct variation. If so, write a direct variation equation for the variation. If not, explain. y x 3 4 5 6 y 4.5 6 7.5 9 3 y x 2 x Direct Variation Direct-Variation Equation Determine whether the values in the table represent a direct variation. If so, write a direct variation equation for the variation. If not, explain. y x y 1 4 2 6 3 8 4 10 x The line did not go through the origin! NOT Direct Variation Determine whether the values in the table represent a direct variation. If so, write a direct variation equation for the variation. If not, explain. y x y -2 -1 4 1 0 0 1 1 x It is not linear! NOT Direct Variation Finding the values and graphing using a direct variation equation At a jumping contest, Evan’s frog jumped 60 inches. Isabella’s frog jumped 72 inches. Jake’s frog jumped 78 inches. Use the equation y=12x, where y is the number of inches and x is the number of feet, to find the missing values in the table. Evan’s Isabell Jake’s frog a’s frog frog Inches (y) Feet (x) 60 72 6 6.5 Finding the values and graphing using a direct variation equation There are 60 minutes in an hour. Find a missing values in the table using the direct variation equation y=60x, where x is the number of hours and y is the number of minutes. Hours (x) Minutes (y) 0 3 360 24 Finding the values and graphing using a direct variation equation Tyler rides his bike at a constant speed of 9mph. Complete the table using the equation y=9x, where x is the number of hours and y is the number of miles he travels. Hours (x) Miles (y) 1 9 1.5 3 45 Create a table, write and equation and graph the direct variation • All spiders have 8 legs. Therefore, 2 spiders have 16 legs, 3 spiders have 24 legs, and so on. • A rose bush grows 3 inches every 4 months. How many inches will it have grown in a year? • Six packs of gum cost $2.00 each. At that rate, how much will 42 packs of gum cost?