### 2.1

```Slope-intercept form: y = mx + b
Ex. 1
a.
Sketch THE graph for each equation
Y = 2x + 1
b.
3x + y = 5
Y = -3x + 5
Slope of horizontal line: 0
Slope of vertical line: undefined
Slope of a line:
yy
xx
Ex. 2
find the slope of the line passing through
each pair of points
a.
(-2, 0) and (3, 1)
1 0
3  2
b.
(3, 4) and (3, 1)
4 1
33


1
5
3
0
 undefined
Point-slope form: y – y1 = m(x – x1)
Ex. 3 find the lope-intercept form of the
equation of the line that has slope of 5 and
goes through (4, -7)
Y – –7 = 5(x – 4)
Y + 7 = 5x – 20
Y = 5x – 27
Slope of parallel lines:
same
Slope of perpendicular lines:
neg. reciprocal
Ex. 4 Find the slope-intercept forms of the equations of the
lines that pass through the point (3, -5) and are (a) parallel
and (b) perpendicular to the line 2x – 3y = 5
2x – 3y = 5
– 3y = –2x + 5
y = 2/3x + 5/3
(B) Perpendicular
y – – 5 = –3/2(x – 3)
(A) Parallel
y – – 5 = 2/3(x – 3)
y + 5 = 2/3x – 2
y = 2/3x – 7
y + 5 = –3/2x + 9/2
y = –3/2x – 1/2
Ex. 5 The maximum recommended slope of a wheelchair ramp
is 1/12. A business is installing a wheelchair ramp that rises 22
inches over a horizontal length of 24 feet. Is the ramp steeper
than recommended?
Ramp is not steeper
1/12 = 0.0833
slope 
vertical change

horizontal change
22 in
 0.076
288 in
Ex. 7 A college purchased exercise equipment worth \$12,000
for the new campus fitness center. The equipment has a useful
life of 8 years. The salvage value at the end of 8 years is \$2000.
Write a linear equation that describes the book value of the
equipment each year.
(0, 12000) and (8, 2000)
slope 
12000  2000
08

10000
8
 \$1250
V – 12000 = –1250(t – 0)
V = –1250t + 12000
Ex. 8 The sales per share for Starbucks Corporation were \$6.97
in 2001 and \$8.47 in 2002. Using only this information, write a
linear equation that gives the sales per share in terms of the
year. The predict the sales per share for 2003.
y – 6.97 = 1.5(x – 1)
y = 1.5x + 5.47
(1, 6.97) and (2, 8.47)
slope 
8.47  6.97
2 1

1.5
 1.5
1
y = 1.5(3) + 5.47
y = 9.97
\$ 9.97 per share in 2003 (estimate based
on our equation)
\$ 10.35 per share in 2003 (actual)
```