Linear Equations and Their Applications

This lesson in 8th grade Eureka Math focuses on linear equations in two variables, building on previous lessons. It covers key vocabulary such as linear equations, standard form, fixed value, and ordered pair. Students learn to use tables to find solutions and graph them. The lesson includes a basketball problem activity to apply these concepts, followed by exercises for practice. It concludes with a real-world application of linear equations and homework instructions.

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

• a + b = c

• x + y = z

• ax + by = c

• x - y = z

Which of the following is an ordered pair?

• x * y

• x - y

• x + y

• (x, y)

In the basketball activity, if Emily scores 32 points with only two-point and three-point baskets, which equation represents this scenario?

• x + y = 32

• x - y = 32

• 3x + 2y = 32

• 2x + 3y = 32

When solving the equation x + y = 3, what is the value of y when x is 2?

• 0

• 2

• 1

• 3

What is the first step in graphing the solutions of a linear equation?

• Choose fixed values for x

• Plot the origin

• Draw the axes

• Solve for y

What is the advantage of starting with the variable that has a coefficient when solving linear equations?

• It makes the calculations more complex.

• It helps in obtaining whole number solutions.

• It ensures the graph is always a straight line.

• It reduces the number of solutions needed.

Why is it beneficial to choose values for the variable with a fractional coefficient that are multiples of the denominator?

• It increases the number of solutions.

• It turns the fraction into a whole number.

• It makes the graph more colorful.

• It ensures the equation has no solution.

In the context of the candy and drinks problem, why is it important to choose values for x that make sense?

• To ensure you buy more candy than drinks.

• To simplify the equation and avoid unnecessary fractions.

• To avoid buying too many drinks.

• To ensure you spend exactly $35.

What is the equation used to represent the relationship between the number of candies and drinks you can buy with $35?

• x + y = 35

• 2x + y = 35

• x + 2y = 35

• 2x + 2y = 35

What should you do if you are unsure about how to choose values for variables in a linear equation?

• Pick random numbers and hope for the best.

• Choose the largest possible numbers to ensure accuracy.

• Look at the coefficients and choose values that simplify the equation.

• Always choose zero for all variables.