PSAT Math Multiple-Choice Practice Test 29: The Heart of Algebra: Linear Equations and Graphs

1. A line, t, is perpendicular to and passes through the point (3, 5). What is the equation of line t ?

A.

B.

C.

D.

2.

In June, Marie notices that the price of gas is increasing. She records the price of gas 4, 8, and 10 months after her initial observation. If y is the price of gas, in dollars per gallon, and x is the number of months after June, which linear equation represents the correct relationship between y and x ?

3.

The graph above shows the volume of a sample of gas as it is cooled. If T is the temperature of the gas in degrees Celsius and V is the volume in liters, which of the following equations, when plotted, could produce the graph shown?

4.

A driving range sells golf balls in different quantities. The figure shows the costs of the various quantities. According to the figure, what is the cost of a single golf ball?

5. Which of the following statements is NOT true if the above equation is true?

A.

B.

C.

D.

6. Line m is parallel to line k and passes through (5, 5). The slope of line k is and line k passes through the origin. Which of the following is the equation for line m?

A.

B.

C.

D.

7. Which value of x makes the equation true?

8.

What is the value of z in the equation above?

A.

B.

C.

D.

9. Sandy works at a tire store. She gets paid $70 for a day's work, plus a commission of $14 for each tire she sells. Which of the following equations represents the relationship between one day of Sandy's pay, y, and the number of tires she sells, x ?

10.

The figure above shows the cost of going to a certain carnival. What does the y-intercept most likely represent?

11. For a car, depreciation is a reduction in value due to use or age. The value of a new car starts to depreciate as soon as the car is purchased and driven for the first time. If the equation y = -0.15x + 27,000 represents the estimated value of a certain car, taking into account depreciation over time, what does 27,000 most likely represent?

12.

What is the value of h in the equation above?

13. A cybercafe is a place that provides Internet access to the public, usually for a fee, along with snacks and drinks. Suppose a cybercafe charges a base rate of $25 to join for a year, an additional $0.30 per visit for the first 50 visits, and $0.10 for every visit after that. How much does the cybercafe charge for a year in which 72 visits are made?

14. An Internet provider charges k dollars for the first hour of use in a month and m dollars per hour for every additional hour used that month. If Jared paid $65.50 for his Internet use in one month, which of the following expressions represents the number of hours he used the Internet that month?

A.

B.

C.

D.