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0600 - Self Test 6
SELF-TEST REVIEW
FOR TEST 6: TWO VARIABLE LINEAR EQUATIONS, SLOPE, GRAPHS AND SQUARE
ROOTS
For 1 and 2 complete each ordered pair so that
it is a solution to the given linear equation:
10) Find the slope of the line given by
3𝑥 − 5𝑦 = 1
1) 𝑥 − 5𝑦 = −1; ( , −2), (4, )
11) Determine if the pair of lines is parallel,
perpendicular or neither.
1
2) 𝑦 = 5 𝑥 − 2; (−10, ), ( ,1)
2
𝑦 = 𝑥−1
5
3) Complete the table of ordered pairs for the
equation 2𝑥 + 𝑦 = 4
x
0
y
0
2
4) Complete the table of ordered pairs for the
1
equation 𝑦 = 2 𝑥 + 3
x
0
-4
5
𝑦=− 𝑥
2
y
0
5.) Plot the following ordered pairs:
𝐴 = (1,2), 𝐵 = (−3,0) and 𝐶 = (−2, −1)
6) Graph the equation 𝑦 = 𝑥 + 5
7) Graph the equation 𝑥 − 3𝑦 = 2
8) Find the intercepts of 2𝑥 + 3𝑦 = 6
9.) Graph the equation y=4
Find the slope of the line that passes through:
12) (−1,16) and (3,4)
13) (−2, −3) and (−2,5)
14) Use slope intercept form to graph
1
𝑦 = 2𝑥 − 2
15) Find the equation of a line where 𝑚 = −3
and 𝑏 = 2
16) Find the equation of a line passing through
(−11, −12) with 𝑚 = −2. Express the
equation in 𝐴𝑥 + 𝐵𝑦 = 𝐶 form.
17) Find the equation of a line passing through
(7,10) and (−1, −1). Express the equation in
𝐴𝑥 + 𝐵𝑦 = 𝐶 form.
18) In 2000, crude oil field production in the
USA was 2130 thousand barrels. In 2007 US
crude oil production dropped to 1850 thousand
barrels.
a) Write two ordered pairs of the form (years
after 2000, crude oil production).
b) Assume the relationship between years after
2000 and crude oil production is linear over
this period. Use the ordered pairs from part (a)
to write an equation of the line relating years
after 2000 to crude oil production.
c) Use the linear equation from part (b) to
estimate crude oil production in the US in
2010, if this trend were to continue.
19) Find √16
27) Find the equation of a line passing through
(-4,3) and (-4, 5).
28) Find the slope of a line which passes
through the points (5,3) and (19,3)
29) Find the slope of a line which passes
through the points (2,1) and (2,-5)
30) Find the slope of a line which is
2
perpendicular to 𝑦 = 3 𝑥 + 2
31) Find the slope of a line which is parallel to
a line a passing through the points (6,-1) and
(-4,-10).
32) A car traveling along a road rises by 16
feet for every 100 feet of horizontal motion.
Find the grade of the road.
33) When walking up a set of stairs one makes
a vertical motion of 16ft and a horizontal
motion of 8 ft. Find the slope of the stairs.
1
20) Find √121
21) Find −√169
22) Find √−36
23) Use the Pythagorean theorem to find x:
7
X
24
24) Simplify: √9 + 16
25) Evaluate √𝑃𝐴 If A=5 and P=20
26) Find the equation of a line passing through
(0,2) and (3,2)
34) Verify that the points (2,1), (0,0) and
(−2, −1) are all on the same line. Do this by
computing the slope between each combination
of points and verify that it is always the same.
35) A student borrows $12,000 from her
parents to buy a car. She plans to pay them
back at the rate of $300 per month.
a.) Write a linear equation to represent the
amount she owes after she makes x payments.
b.) How many months will it take to pay off
the loan?
Answers:
1) (−11, −2), (4,1)
2) (−10, −4), (15,1)
3)
x
y
0
4
2
0
1
2
8) (0,2), (3,0)
9)
4)
X
0
-4
-6
y
3
1
0
3
10) 𝑚 = 5
11) Perpendicular
12) 𝑚 = −3
13) Undefined slope
14)
5)
y
.A
x
.B
.C
6)
7)
15) 𝑦 = −3𝑥 + 2
16) 2𝑥 + 𝑦 = −34
17) 11𝑥 − 8𝑦 = −3
18) a) (0,2130), (7,1850)
b) 𝑦 = −40𝑥 + 2130
c) 1730 thousand barrels
19) 4
20) 1/11
21) -13
22) not a real number
23) X=25
24) 5
25) 10
26) Horizontal line 𝑦 = 2
27) Vertical line 𝑥 = −4
28) Slope is 0
29) Slope is undefined
30) Slope is -3/2
31) Slope is 9/10
32) 16%
33) Slope is 2
34) Slope is always ½
35) a) 𝑦 = −300𝑥 + 12000 b) 40 months
0600 Self Test6
Created for fall 2014