Writing Equations with Two Variables

In this video, Jeff Jacobson introduces equations with two variables, explaining the relationship between independent and dependent variables. He demonstrates how to graph these equations and verify solutions using ordered pairs. Through examples, including a real-world milk jug problem, viewers learn to identify variables and solve equations. The video concludes with practice problems to reinforce learning.

What is the key characteristic of equations with two variables?

• They do not have any solutions.

• They represent two quantities that change in relationship to one another.

• They represent two quantities that change independently.

• They have only one solution.

Which variable can change freely in an equation with two variables?

• Both variables

• Independent variable

• Neither variable

• Dependent variable

In the context of equations with two variables, what does the dependent variable depend on?

• The product of both variables

• The sum of both variables

• The value of the dependent variable

• The value of the independent variable

Which axis typically represents the independent variable in a graph?

• Y-axis

• Z-axis

• X-axis

• W-axis

What is an ordered pair in the context of equations with two variables?

• A pair of unrelated values

• A pair of values that work together as a solution

• A pair of dependent variables

• A pair of independent variables

If the ordered pair (3, 6) is substituted into the equation y = 2x, is it a solution?

• Yes, because 6 equals 2 times 3

• No, because 6 does not equal 2 times 3

• Yes, because 3 equals 2 times 6

• No, because 3 does not equal 2 times 6

For the equation y = 4x - 3, is the ordered pair (4, 12) a solution?

• Yes, because 12 equals 4 times 4 minus 3

• No, because 12 does not equal 4 times 4 minus 3

• Yes, because 4 equals 4 times 12 minus 3

• No, because 4 does not equal 4 times 12 minus 3

In the equation y = 128 - 8x, what does the number 128 represent?

• The number of fluid ounces in a cup

• The total amount of milk in a full jug

• The amount of milk left in fluid ounces

• The number of cups of milk poured out

In the equation y = 128 - 8x, what is the independent variable?

• Y, the amount of milk left

• 128, the total amount of milk

• 8, the number of fluid ounces in a cup

• X, the number of cups poured out

How much milk is left after pouring out 10 cups, given the equation y = 128 - 8x?

• 10 fluid ounces

• 48 fluid ounces

• 128 fluid ounces

• 80 fluid ounces