Instructions: (100 points) Solve each problem and
box in your final answer .
1. Short responses.
(a) Name the possible quadrants in which the point (x, y) can lie if
| I only |
II only |
III only |
IV only |
| I or III √ |
I or IV |
II or IV |
II or III |
(b) Given an equation in the variables x and y, to
find the y- intercepts in the equation you set the variable x
equal to zero and solve for y .
(c) T (True/False) Given a function y = f
(x), to test for y-axis symmetry you verify that the function f
satisfies the equation f (x) = f (−x).
(d) The slope of the line passing through the two
points P(−4,−3) and Q(5, 0) is m = 1/3 .
(e) The line given by the equation 3x − 2y = 4 has a
slope of m = 3/2 .
(f) Are the lines 2x + 3y = 6 and 6x − 4y = 5
perpendicular?
Yes, perpendicular√
No, not perpendicular
(g) Which of the fol lowing is not true for the
number of solutions to a system of linear equations can have:
no solutions
one solution
two solutions √
infinitely many solutions
2. Find the distance between P(−3,−3) and Q(1, 4).
d(P,Q) =
Solution: Apply the distance formula :
3. Suppose P(13, 5) is the endpoint of a segment PQ and
M(−2,−4) is
the midpoint of the segment PQ. Find the coordinates of the endpoint
Q.
Solution: We set up a couple of equations, and
solve. Because the midpoint is calculated by
We equate
4. Give the domain and range of the relation { (0, 5), (1,
3), (0,−4) } and state whether the relation is a function
Domain= {0, 1}
Range= {5, 3,−4}
F (True/False) This relation is a function.
5. A line of slope −1/2 passes through the point P(2, 1),
find the equation of the line. Leave your answer in the
slope-intercept form. Also, make a good sketch of the line—labeling the x- and
y-intercepts—on the coordinate
system to the right.
Solution: We use the point-slope version of the
equation of a line:
6. Solve each of the following concerning the line
and the point P(−1, 4).
(a) Find the equation of the line
passing through P and
parallel to the line  .
Solution: We use the point-slope version of the equation
of a line with m = 3:
 |
(b) Find the equation of the line
passing through P and
perpendicular to the line .
Solution: We use the point-slope version of the equation
of a line with m = −1/3:
 |
7. Solve the equation −(8 + 3x) + 5 = 2x + 3 for x, and
leave your answer as a solution set .
Solution set =
Solution: We solve this linear equation:
8. A student needs a 10% solution of hydrochloric acid for
a chemistry experiment. How much 5% acid should be
mixed with 120 milliliters of 20% to get the 10% solution? Let x be the amount
of 5% acid needed.
x = 240mL
Solution: We describe, in the form on an equation,
the conditions of this problem.
