6 1. REVIEW OF ALGEBRA
Problem 1.8 Solve the following equations for x.
1. y D
7x C 6
4x C 3
2. y D
9x 6
x C 1
3. y D
4x C 2
3x C 3
4. y D
4x 3
9x C 9
5. y D
4x 3
4x C 4
6. y D
2x 1
5x C 4
Problem 1.9 Solve for i: N i D Kq
Problem 1.10 Solve for a: mua D n
Problem 1.11 Solve for K:
1
o
D
KO
r
Problem 1.12 Solve for U:
IL
F c
D U
Problem 1.13 Solve for z:
1
D
D
nM
z
Problem 1.14 Solve for i:
1
ni
D
XJ
e
Problem 1.15 Solve for n: Y V D
1
gn
Problem 1.16 Solve for U:
F
D
D
1
U n
1.2 LINES
We will start with an example of a very simple line: y D x C 1 (Figure 1.1). For any value of x
we add one to x and get y. We can draw the line by picking any two points on it, lining up a
straight edge on the two points, and drawing along the straight edge.
e line y D x C 1 is made of all the points that look like .x; x C 1/. Five points like that have
been plotted in Figure 1.1: (-2,-1), (-1,0), (0,1), (1,2), and (2,3).
Definition 1.1 A line can always be written in the form y D mx C b where m is the slope of the
line, and b is the y-intercept of the line. Both m and b are numbers.
ere are different ways to interpret the parameters m and b.
• e number m is the amount the y-value increases for each increase of 1 in the x-value.
• If we pick two points on the line, then the run between those points is the change in the
x-value, and the rise is the change in the y-value. e slope, m, is the rise divided by the
run.
• e y-intercept b is where the line hits the y-axis. is means the point .0; b/ is on the
line.
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