Independent and Dependent Variables with Math and Graphs

Consider the relation {(x, y) | y = x^2}. Is this a function?

• Yes, because for each x, there is only one y.

• No, because x can have multiple values for y.

• Yes, because x is positive.

• No, because it’s not a linear relation.

A teacher conducts an experiment where students study for different amounts of time and then take a math test. She records their scores. What conclusion can she make about the independent and dependent variables?

• The independent variable is the test scores, and the dependent variable is the study time.

• The independent variable is the study time, and the dependent variable is the test scores.

• Both study time and test scores are independent variables.

• The study time has no impact on the test scores, so there are no dependent or independent variables.

Which of the following best describes the relationship between independent and dependent variables?

• The dependent variable is what you change, and the independent variable responds.

• The independent variable is what you change, and the dependent variable responds.

• Both the independent and dependent variables change randomly.

• Both variables remain constant.

Which of the following is the label for the independent variable.

• Money Collected

• Raising Money

• Boxes Sold

• None of the above

Match the following using the given graph of a two-variable equation.

• 5 seconds

• Independent Variable y

• y = 4x

• Dependent Variable x

• Time in seconds

• Time it takes to reach a velocity of 20 m/s

• 8 m/s

• Velocity after 2 minutes

• Velocity in m/s

• Equation

Choose the correct equation for the given graph.

• y = x + 2

• y = 4 + x

• y = x - 2

• y = 4 - x

Answer explanation

As we can see in the graph that the line is intersecting x axis at 2 and y axis at -2. So here we have got two points (2, 0) and (0, -2). Now let's substitute these points in y = x - 2 (2, 0) In LHS, y = 0 In RHS, x - 2 = 2 - 2 = 0 So, LHS = RHS (0, -2) In LHS, y = -2 In RHS, x - 2 = 0 -2 = -2 So, LHS = RHS Therefore, The graph in the figure is of the equation y = x - 2 and option 3 is the correct answer.

Which label best describes the independent quantities shown in the table?

• Number of tickets (t)

• Cost (c)

On a graph, which axis shows the dependent variable?

• x-axis

• y-axis

• neither

• it changes

On a graph, which axis shows the independent variable?

• x-axis

• y-axis

• neither

• it changes

A(n) _____________ variable depends on or is changed by another variable.

• dependent

• independent