Math 125
Exam 2
Solve, if possible. If the equation is an identity or contradiction, then indicate so.
3
1) - 12p =
4
3
1
4 12
p=
p=-
2) 2x -
1
16
5 11
=
9 27
27 2x -
5
11
=
27
9
27
54x - 15 = 11
54x = 26
x=
26
54
x=
13
27
3) 2p + 3 p - 3 = 7 + 5p
2p + 3p - 9 = 7 + 5p
5p - 9 = 7 + 5p
-9=7
contradiction
1
4) -
2
5
4
x+2= x+
3
6
5
30 -
2
5
4
x + 2 = x + 30
3
6
5
- 20x + 60 = 25x + 24
36 = 45x
36
=x
45
x=
4
5
5) 8x - (6x - 13) = 2
2x + 13 = 2
2x = - 11
x=-
6)
11
2
1
1
(20x - 25) = (15x - 12)
5
3
4x - 5 = 5x - 4
-1=x
Solve the literal equation for the specified variable.
w+y+z
for y
7) x =
8
x=
w+y+z
8
8x = w + y + z
8x - w - z = y
2
Plot the points on the rectangular coordinate plane. Identify the quadrant of each point, if applicable.
8) (2, 5), (-6, 0)
(2, 5) is in quadrant I
Find the coordinates of the labeled points. Identify the quadrant of each point, if applicable.
9)
A(6, 5) is in quadrant 1, B(0, -6)
Using the given coordinate, find the other coordinate that makes the ordered pair a solution of the equation.
1
10) x + 3y = -17, (-35, y)
7
1
(-35) + 3y = -17
7
- 5 + 3y = - 17
3y = - 12
y=- 4
3
Find and identify the intercepts; then graph the line using the intercepts ONLY. Find and identify the slope.
11) 2x - 3y = - 18
- 18
= - 9 - 9, 0 x-intercept
2
- 18
2
2
= 6 0, 6 y-intercept m = =
-3
-3 3
Find and identify the intercepts; then graph. Find and identify the slope.
12) x = -3
slope is undefined; (- 3, 0)
Provide an appropriate response.
13) Find the equation of a line that is parallel to 5y = 20 and has a y-intercept at 0, -4 .
y = -4
Find the slope-intercept form of the equation of a line that passes through the given points.
14) (-4, 7), (9, -7)
m=
7--7
14
=
- 4 - 9 - 13
y-7=-
14
x--4
13
y=-
14
56 91
x+
13
13 13
y=-
14
35
x+
13
13
4
Find the standard form of the equation of a line perpendicular to the given line and passing through the given point.
15) Perpendicular to 3x - 7y = -22, through (9, -7)
m=-
3
3
=
-7 7
y--7=-
7
x-9
3
3y+7 =-
7
x-93
3
3y + 21 = - 7 x - 9
3y + 21 = - 7x + 63
7x + 3y = 42
5