Comparing Linear Representations

The graph shows the acres of corn a farmer has left to plant. The equation A = 4,000 – 180d gives the acres of soybeans a neighbor has left to plant as a function of time in days. Which statement is true?

• Both farmers have 4,000 acres to plant on Day 0.

• The corn farmer plants more acres per day than the soybean farmer.

• The corn farmer will finish planting first.

• From days 1–20, the soybean farmer always has more to plant.

If two increasing linear functions have the same rate of change and different initial values, their graphs will intersect.

• Always

• Sometimes

• Never

Tell whether the statement is Always, Sometimes, or Never true.

If the graphs of two linear functions intersect, one function has a positive rate of change and one function has a negative rate of change.

• Always

• Sometimes

• Never

Tell whether the statement is Always, Sometimes, or Never true.

If two proportional relationships have the same rate of change, they are the same function.

• Always

• Sometimes

• Never

Tell whether the statement is Always, Sometimes, or Never true.

The graphs of a linear function and a nonlinear function intersect exactly once.

• Always

• Sometimes

• Never

Functions A and B are both linear. Which statement comparing the functions is true?

• The slope of Function A is equal to the slope of Function B

• The slope of Function A is less than the slope of Function B.

• The y-intercept of Function A is equal to the y-intercept of Function B.

• The y-intercept of Function A is less than the y-intercept of Function B.

Two families go on vacation and each take a different route. The families record the average speeds of their routes as a relationship of distance (miles) and time (hours). The relationship of distance, d, and time, t, is represented differently for each person. Which TWO statements are true?

• The Smith family and Johnson family begin with equal initial distances.

• The Smith family begins with a greater initial distance than the Johnson family.

• The Smith family travels travels at a rate of 8 miles per hour faster than the Johnson family.

• The Johnson family begins with a greater initial distance than the Smith family.

• The Johnson family travels at a rate 8 miles per hour faster than the Smith family.

The rate of change is constant in the table. Find the rate of change. Explain what the rate of change means for the situation.

Which of the following statements is true concerning the graph below?

• The slope is 1

• The slope is

• The slope is -1

Which table represents a linear function?

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