Math 1090
Quiz 1 Solution
January 26th, 2015
Answer the following 4 questions in the space provided. The value of every
question is indicated at the beginning. Time: 10 minutes.
Name:
UID:
1. (5 points) Find the slope and the y-intercept of the line 2x + 7y = 3.
Solution. The point here is to solve for y, namely to obtain an expression of the form
y = mx + b. Then m will be your slope, and (0, b) will be your y-intercept. In this case
we have
2x + 7y = 3
7y = −2x + 3
2
3
y =− x+
7
7
So the slope is m = − 27 and the y-intercept is the point 0, 73 .
2. (5 points) Find the equation of the line that passes through the point (−3, 8) and is
perpendicular to the line from question 1.
Solution. Remember that two lines are perpendicular if their slopes m1 and m2 satisfy
the relation m2 = − m11 . Since the line from question 1 has slope m1 = − 27 , a line
perpendicular to it must have slope m2 = − m11 = − −12 = 72 .
7
We thus need to find the equation of a line with slope 27 that passes through the point
(−3, 8). Using the point-slope formula, the equation will be
7
y − 8 = (x − (−3))
2
7
y − 8 = (x + 3)
2
3. (5 points) Is the line that goes through the points (−3, 8) and (4, 6) parallel to the line
from question 1?
Solution. Remember that 2 lines are parallel if they have the same slope. The slope of
the line from question 1 was m = − 27 .
The slope of the line that goes through two points (x1 , y1 ) and (x2 , y2 ) is given by
y2 − y1
m=
x2 − x1
so for the points (−3, 8) and (4, 6) we have
m=
6−8
2
=−
4 − (−3)
7
Since both slopes coincide, the 2 lines are parallel.
4. (5 points) Find 3 consecutive integers whose sum is 36.
Solution. We can write three consecutive integers as a, a + 1 and a + 2, where a is some
integer. We need to find an integer a such that
a + (a + 1) + (a + 2) = 36
3a + 3 = 36
3a = 33
a = 11
so a = 11 is your solution.
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