Linear Equations and Their Applications

This lesson covers linear equations in two variables, explaining their standard form and how to solve them by fixing one variable. It includes examples like a basketball scoring problem and demonstrates graphing solutions on a coordinate plane. The lesson also provides practice problems and applies linear equations to word problems, such as budgeting for snacks.

What is the standard form of a linear equation in two variables?

• xy = ab

• a + b = c

• x + y = z

• ax + by = c

In the example of Emily's basketball game, how many points did she score using only two-point shots?

• 16 points

• 28 points

• 32 points

• 30 points

When plotting solutions on a coordinate plane, which axis represents the x variable?

• Vertical axis

• Horizontal axis

• Diagonal axis

• None of the above

If x + y = 3, what is the value of y when x is 1?

• 3

• 0

• 1

• 2

In the equation 2x + y = 10, what is y when x is 1?

• -8

• 8

• 0

• 10

For the equation x + 5y = -21, why might it be easier to choose values for y instead of x?

• Because x is a constant

• Because y is a variable

• Because dividing by 5 is not always even

• Because y is always positive

What is the result of multiplying two-fifths by 10?

• 10

• 4

• 5

• 2

In the candy and drinks example, what is the equation representing the total cost?

• 2x + y = 35

• x + 2y = 35

• x + y = 35

• 2x + 2y = 35

What is the total number of points Emily scored in the basketball game example?

• 34

• 28

• 32

• 30

What is the main takeaway from the lesson on linear equations in two variables?

• They can be represented as a straight line on a graph

• They always have one solution

• They have no real-world applications

• They are only used in sports