Which situation best represents the linear equation y = 3x + 5?

A. A biologist began an experiment with one unit of bacteria. The bacteria doubled in size each week. What is y, the number of units of bacteria, after x weeks?
Incorrect. Since the bacteria double in size each week, this is not a linear relationship and would not be represented by the given equation.

B. The height of each successive bounce of a certain ball is 50% of the previous bounce height of the ball. What is y, the height of the x bounce, of this ball?
Incorrect. Since the height of the bounce is 50% less than the previous bounce height, this is not a linear relationship and would not be represented by the given equation.

C. A botanist records the height of new variety of rose. She expects the average growth rate to be three centimeters each week. If the plant was five centimeters tall when the botanist began measuring, what is y, the height of the rose, after x weeks?
Correct! Since the height of the plant was 5 cm when the weekly measuring began and the height increases by 3 cm each week, this does represent the given equation.

D. The length of a garden is five feet more than the width. What is y, the area of the garden, if the width is x feet?
Incorrect. Since area is the product of the length and the width and both are unknown, this is not a linear relationship and would not be represented by the given equation.

Which problem situation best represents the linear equation y = 4x?

A. Jason drew a square on grid paper. What is y, the perimeter of the square, if each side of the square measures x inches?
Correct! Since each side of the square measures the same length, x, then the perimeter, y, is represented by 4x.

B. The length of a rectangle is four feet more than the width. What is y, the area of the rectangle if the width is x feet?
Incorrect. Since the area is the product of the length and the width and both are unknown, this is not a linear relationship and would not be represented by the given equation.

C. Ade receives a 4% cost of living increase each year. What is y, his annual salary, if he makes x dollars per year?
Incorrect. 4% would be written as the decimal 0.04 in order to write the equation.

D. Cecil is four years older than his sister. What is y, the sum of their ages, if his sister is x years old?
Incorrect. Since Cecil is 4 years older than his sister, addition is the correct operation not multiplication.

Which problem situation best represents the equation y = 2x + 10?

A. The length of a rectangle is 10 more than twice its width. What is y, the perimeter of the rectangle, if the width is x centimeters?
Incorrect. To find the perimeter you would need to add all 4 sides of the rectangle.

B. The number of girls in the choir is 10 more than the number of boys. If there are x boys in the choir, how many total students, y, are in the choir?
Correct! The number of boys, x, plus the number of girls, x + 10, would equal y, the total number of students in the choir.

C. Mr. Galvan drove twice as many miles on Monday as he did on Tuesday. What is y, the total distance Mr. Galvan drove, if he drove x miles on Tuesday?
Incorrect. This equation does not take into account the “plus 10” that is in the equation.

D. The base of an isosceles triangle is 10 more than the twice the length of one of the legs. What is y, the perimeter of the triangle, if the length of the leg is x inches?
Incorrect. To find the perimeter, you would need to add the lengths of 2 legs and the base.

Which problem situation does NOT represent the equation y = 36 − 4x?

A. At an amusement park each food item cost $4 each. If Dave began the day with $36, how much money, y, does he have after buying x food items?
Incorrect. This situation does represent the given equation.

B. Mr. Cisneros had 36 inches of wire to complete several project. If he uses x inches of wire for 4 projects, how much wire, y, does he have left?
Incorrect. This situation does represent the given equation.

C. A square has a perimeter of 36 inches. What is the y, the perimeter of the square, if each side measures x inches?
Correct! The equation that represents this situation would be y = 4x.

D. Yusef had $36 in his savings account. He withdrew $4 each month for x months. How much money, y, is left in his savings account.
Incorrect. This situation does represent the given equation.