show a relationship as an equation, table, or graph
Review Coordinate plane
Let's take a moment to review graphing on the coordinate plane. The table below lists values for x and y. Recall how to write the values as an ordered pair and plot them on the graph.
COORDINATE PLANE
ordered pair
y-axis
(x, y)
(0, 0)
Click each button on the table to reveal the ordered pair an plot the point
(2, 1)
(4, 2)
(6, 3)
(8, 4)
x-axis
origin
*Notice that each point can be connected in a straight line. This can be drawn to further see the relationship between x and y.
AnaLyzing Graphs
We can use graphs to create a table and an equation relating two variables. Consider the graph below which relates the distance and time of a bike rider:
Bike rider's speed
Distance (miles)
Time (hours)
Click each button on the graph to fill in the table
Distance in miles (y)
15
30
dependent variable
45
60
Let x = time in hours and y = distance in miles
Time in hours (x)
independent variable
Our equation multiplies speed by time to get distance:
15
*Notice that for each hour, the bike rider travels miles. So the rate or speed is miles per hour.
15
y = 15x
AnaLyzing Graphs
There will be times when the x value will change by a value other than 1. Consider the example below showing a bike racer going a bit faster. How can we find the equation here?
Bike racer's speed
Distance (miles)
Time (hours)
Distance in miles (y)
Click each button on the graph to fill in the table
50
dependent variable
100
150
200
independent variable
Let x = time in hours and y = distance in miles
Time in hours (x)
Our equation multiplies speed by time to get distance:
*Speed is a unit rate of distance over time. We can divide one of the distances by its time to get the speed:
y = 25x
50 miles ÷ 2 hours = 25 miles per hour
AnaLyzing Graphs
Find the equation for the graph below that measures a riding mower's distance over time.
Lawn Mower's Speed
Distance (miles)
Time (hours)
Distance in miles (y)
24
Click each button on the graph to fill in the table
48
dependent variable
72
96
independent variable
Let x = time in hours and y = distance in miles
Time in hours (x)
Our equation multiplies speed by time to get distance:
*Speed is a unit rate of distance over time. We can divide one of the distances by its time to get the speed:
y = 12x
24 miles ÷ 2 hours = 12 miles per hour
AnaLyzing Graphs
You can use the equation to find other values on the graph. Using the lawn mower example:
Distance in miles (y)
Our equation multiplies speed by time to get distance:
y = 12x
* we can pick different values for time (x), plug them into our equation and calculate distance.
Lawn Mower's speed
dependent variable
*See if you can fill in the rest of the table below using the various times for x! click the buttons to reveal the missing values
Analyzing Relationships
Simon Ainsworth
Created on July 18, 2024
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Transcript
Module 4
Analyzing Relationships
Lesson 7
Start
Goals
Objectives:- analyze relationships using graphs
- show a relationship as an equation, table, or graph
Review Coordinate plane
Let's take a moment to review graphing on the coordinate plane. The table below lists values for x and y. Recall how to write the values as an ordered pair and plot them on the graph.
COORDINATE PLANE
ordered pair
y-axis
(x, y)
(0, 0)
Click each button on the table to reveal the ordered pair an plot the point
(2, 1)
(4, 2)
(6, 3)
(8, 4)
x-axis
origin
*Notice that each point can be connected in a straight line. This can be drawn to further see the relationship between x and y.
AnaLyzing Graphs
We can use graphs to create a table and an equation relating two variables. Consider the graph below which relates the distance and time of a bike rider:
Bike rider's speed
Distance (miles)
Time (hours)
Click each button on the graph to fill in the table
Distance in miles (y)
15
30
dependent variable
45
60
Let x = time in hours and y = distance in miles
Time in hours (x)
independent variable
Our equation multiplies speed by time to get distance:
15
*Notice that for each hour, the bike rider travels miles. So the rate or speed is miles per hour.
15
y = 15x
AnaLyzing Graphs
There will be times when the x value will change by a value other than 1. Consider the example below showing a bike racer going a bit faster. How can we find the equation here?
Bike racer's speed
Distance (miles)
Time (hours)
Distance in miles (y)
Click each button on the graph to fill in the table
50
dependent variable
100
150
200
independent variable
Let x = time in hours and y = distance in miles
Time in hours (x)
Our equation multiplies speed by time to get distance:
*Speed is a unit rate of distance over time. We can divide one of the distances by its time to get the speed:
y = 25x
50 miles ÷ 2 hours = 25 miles per hour
AnaLyzing Graphs
Find the equation for the graph below that measures a riding mower's distance over time.
Lawn Mower's Speed
Distance (miles)
Time (hours)
Distance in miles (y)
24
Click each button on the graph to fill in the table
48
dependent variable
72
96
independent variable
Let x = time in hours and y = distance in miles
Time in hours (x)
Our equation multiplies speed by time to get distance:
*Speed is a unit rate of distance over time. We can divide one of the distances by its time to get the speed:
y = 12x
24 miles ÷ 2 hours = 12 miles per hour
AnaLyzing Graphs
You can use the equation to find other values on the graph. Using the lawn mower example:
Distance in miles (y)
Our equation multiplies speed by time to get distance:
y = 12x
* we can pick different values for time (x), plug them into our equation and calculate distance.
Lawn Mower's speed
dependent variable
*See if you can fill in the rest of the table below using the various times for x! click the buttons to reveal the missing values
Multiply time by speed
Distance in miles (y)
Time in hours (x)
14.4
y = 12 • 1.2 =
1.2
30
y = 12 • 2.5 =
2.5
36
y = 12 • 3 =
45.6
y = 12 • 3.8 =
3.8
Time in hours (x)
independent variable
64.8
5.4
y = 12 • 5.4 =