Questions on Linear Functions
This page contains sample problems on linear functions. They
are for Self-assessment and Review.
problem (or group of problems) has an "answer button" which you
can click to look at an answer. Some solutions have a
"further explanation button"
which you can click to see a more complete, detailed
What to Do To gain
the most benefit from these problems,
problems on your own. Write down your solutions BEFORE
looking at any answers.
Use a graphing calculator as
appropriate. A graphing calculator can be used to verify
that your answers "make sense" or "look right".
have difficulties with this material, please contact your
instructor. (See Getting Help
in Stage 1.) It will be very difficult to succeed in
Calculus without being able to solve and manipulate linear
1. Find the slopes and the x- and y-intercepts of the
- y + 3 = -2 (x - 5)
y = 1.2 x - 7
3 x - 5 y = 20
y - c = 2 x + c/2
2. In economics the demand
function relates the price per unit of an item to the number of units that consumers will buy at that price. The demand, q, is considered to be the independent variable, while the price, p, is considered to be the dependent variable.
Suppose that in a certain market, the demand function for widgets is a linear function
p = -0.75q + 54,
where p is the price in dollars and q is the number of units
(hundreds of widgets
in this case).
- What is the slope of this function? Explain the meaning of the
sign of the
slope in practical terms.
Find the p- and q- intercepts for this function. What is the
of these intercepts in the context of the problem?
3. State whether the following pairs of lines are parallel,
- y = (3/2)x -7 and 3x - 2y = 4
- 5x - 3y = 12 and 3x + 5y = 10
- x - y = 10 and x + y = -1
- x - 2y = 1 and 2x - y = 5
- x - 3y = 5 and -2x + 6y = 8
- 3x + 7y = 9 and -6x + 14y = 21
- y = (2/5)x + 2 and 5x - 2y = -4
- x = 10 and y - 10 = 0
4. Find the equation of each of the following lines:
- The line with slope -1/2 and passing through the point (0,
- The line with slope -2/3 and containing the point (6, -1).
- The line passing through the points (7, -1) and (4, 5).
- The line with slope 6 and passing through the graph of f(x) =
x2 where x = 3.
- The line passing through (4,0) and the graph of f(x) =
x2/3 where x = -8.
- The line perpendicular to 3x + y = 17 and passing through ( 15,
5. A small college has 2546 students in 1994 and 2702
students in 1996. Assume
that the enrollment follows a linear growth pattern. Let t = 0
1990 and let y(t) represent the enrollment in year t.
- Assume that y(t) is linear. Using the data given, find the
slope of y(t).
- What does the slope of y(t) signify in terms of enrollment
- Find an equation for y(t) and use it predict the enrollment of the
college in 1999.
6. Find the point(s) of intersection of each of the following
pairs of lines.
- 2 x - y = 10 and x + y = -1
- y = 2 x + 5 and y - 1 = 2 (x -3)
- y = (2/3) x + 5 and 2 x - 3 y = -15
- 3 x + 3 y = 180 and 3.6 x - 3.6 y = 180