Exploring the Standard Form of Linear Equations

What is the standard form of an equation?

• An equation where all variables are on one side and the constant is on the other.

• An equation where variables and constants are mixed on both sides.

• An equation that cannot be graphed.

• An equation with only one variable.

In the problem involving Cheryl's basketball game, what do the variables x and y represent?

• x represents total points and y represents free throws.

• x represents two-point baskets and y represents three-point baskets.

• x represents free throws and y represents three-point baskets.

• x represents three-point baskets and y represents two-point baskets.

What is the equation in standard form for Cheryl's total points?

• 2x + 3y = 27

• 2x - 3y = 27

• 3x + 2y = 27

• x + y = 27

What are the coordinates if Cheryl made no two-point baskets?

• (0, 27)

• (0, 9)

• (9, 0)

• (27, 0)

Why is the coordinate (13.5, 0) not possible in the context of the problem?

• Because x must be less than 10.

• Because 13.5 is not a whole number.

• Because Cheryl cannot score 13.5 points.

• Because y must be greater than 0.

What is the third coordinate used to ensure the graph's accuracy?

• (6, 5)

• (7, 3)

• (5, 6)

• (3, 7)

Which combination of baskets is possible according to the graph?

• 3 two-point baskets and 7 three-point baskets

• 4 two-point baskets and 6 three-point baskets

• 5 two-point baskets and 5 three-point baskets

• 6 two-point baskets and 4 three-point baskets

What is the greatest number of three-point shots Cheryl may have made?

• 8

• 9

• 10

• 7

What is the greatest number of two-point shots Cheryl may have made?

• 10

• 11

• 12

• 13

Why is it important to use whole numbers for x and y in this problem?

• Because the total points must be a whole number.

• Because the equation requires whole numbers.

• Because baskets cannot be made in fractions.

• Because the graph only accepts whole numbers.