Expressions Equations Dependent vs Independent variables 1 2013

Objective: You will be able to… �Explain what an independent variable is in your own words �Explain what a dependent variable is in your own words �Write equations showing the relationship between the independent and dependent variables �Analyze the relationship between an independent and a dependent variable using graphs and tables and relate it to an equation 2 © 2013 Meredith S. Moody

Vocabulary �Independent variable: A variable that determines the value of other variables �Dependent variable:

Independent variables �Independent variables are things that don’t depend on something else �For example, time is an independent variable �No matter what happens, time occurs �Nothing influences time 4 © 2013 Meredith S. Moody

Dependent variables �Dependent variables are things that change when something else happens �For example, your age is a dependent variable �It changes with time; as time passes, your age increases �Age is a dependent variable – how old is someone? It depends on the time (time of day, week, month, year, etc. ). 5 © 2013 Meredith S. Moody

Independent vs. dependent variables �How can you tell if a variable is independent or dependent? �Does it depend on something else? �If you can answer “it depends on…” then your variable is dependent �How long will it take John to drive to the store? �It depends on how fast he is driving �It depends on how far away the store is 6 © 2013 Meredith S. Moody

Example: Driving � John lives in Texas; his friend lives in New York � John is going to drive to New York to visit his friend � How far will John have driven after one day of driving? � It depends on…his speed � John drives 70 miles per hour his first day of driving � How far has he gone after one day of driving? � It depends on…how long he drives � John drove for 8 hours his first day of driving � John drove 70 miles per hour for 8 hours � His first day of driving, John drove 8 x 70 = 560 miles 7 © 2013 Meredith S. Moody

Example: Graphing John’s trip �If John drove 70 miles per hour for 8 hours, how far had he gone before lunch? �Use the graph of John’s time and distance �John ate lunch after he had driven 4. 5 hours �John traveled a little more than 300 miles before lunch 8 © 2013 Meredith S. Moody

Graphing rules �When graphing independent-dependent variable relationships, the independent variable ALWAYS goes on the x-axis �The dependent variable ALWAYS goes on the y-axis �How to remember: time is ALWAYS independent; time moves forward (horizontal, x-axis), not up (vertical, y-axis) 9 © 2013 Meredith S. Moody

Example: Science applications �Another subject that uses dependent and independent variables is science �In an experiment, there is an independent variable �For example, if a scientist wants to know how fertilizer affects plant growth, the fertilizer would be the independent variable �The growth would be the dependent variable �How high the plant grows would depend on how much fertilizer each plant receives 10 © 2013 Meredith S. Moody

Example: Graphing plant growth �The height of the plant depends on how much fertilizer is used �This chart shows the relationship between fertilizer and growth �How high did a plant that got 2. 5 grams of fertilizer grow? �The plant grew about 2. 5 inches tall 11 © 2013 Meredith S. Moody

Check! �Write down, in your own words, what an independent variable is �Share your explanation with a neighbor �Write down, in your own words, what a dependent variable is �Share your explanation with a different neighbor 12 © 2013 Meredith S. Moody

Guided practice � Identify which variable in the following scenarios is independent and which is dependent � Katy drives 30 miles per hour on her way to work; how far has she driven after half an hour? �Her distance depends on how long she drives and her speed (30 mph) �Independent variable: time (half an hour) & speed (30 mph) �Dependent variable: distance � A scientist wants to know how the temperature changes overnight; what is the temperature at 11 pm? �The temperature depends on the time of night �Independent variable: time �Dependent variable: temperature 13 © 2013 Meredith S. Moody

Guided practice: graphing � Katy drives 30 miles per hour to work � How far has she driven after half an hour? � Independent variable: speed (30 mph) � Independent variable: time (half an hour) � Dependent variable: distance � x-axis: time/speed � y-axis: distance � She has traveled 15 miles after half an hour 14 © 2013 Meredith S. Moody

Example: Equations (John) �Relationships between independent and dependent variables can be written as equations �John drove 70 miles per hour; how far he went depended on how long he drove �John’s distance was his speed for however long he drove �His distance (d) equaled 70 mph x his time (t) �d = 70 t �Why multiplication? �It is repeated addition; if John drove for 2 hours, his distance would be 70 + 70, or 70 x 2 15 © 2013 Meredith S. Moody

Example: Equations (Katy) �Katy drove 30 miles per hour �Her distance was 30 miles per hour for however long she drove �After 1 hour, she had driven 30 miles; after 2 hours, 60 miles �Her distance (d) equaled 30 mph x her time (t) �d = 30 t 16 © 2013 Meredith S. Moody

Guided practice: Equations �A scientist wants to measure the effect of water on plant growth �He conducts an experiment and notices that for ever 2 oz of water he gives a plant, it grows 1 inch �The height (h) of the plant is twice the oz of water (w) he gives it �The height equals 2 times the oz of water �h = 2 w 17 © 2013 Meredith S. Moody

Guided practice: Plants and water �The graph of a relationship relates to the equation �A plant grows 1 inch for every 2 oz of water �The height depends on the amount of water �water: x-axis �height: y-axis �Height is 1 in for every 2 oz �h = 2 w 18 © 2013 Meredith S. Moody

You try! �Jim drives 15 miles per hour in the city �How far has he driven after 1. 5 hours? �Identify the independent and dependent variables �Graph the relationship �Write an equation for the relationship 19 © 2013 Meredith S. Moody