200 CHAPTER 3 Graphs, Linear Equations, and Functions
3.1 The Rectangular Coordinate System
Finding Intercepts
To find the x-intercept, let and solve for x.
To find the y-intercept, let and solve for y.
Midpoint Formula
If the endpoints of a line segment PQare and
, then its midpoint Mis
ax 1 x 2
2,
y 1 y 2
2b.Q 1 x 2 , y 22
P 1 x 1 , y 12x= 0y= 0Find the intercepts of the graph ofThe x-intercept is The y-intercept isFind the midpoint of the segment with endpoints and
.a4 + 1 - 102
2
,
- 7 + 1 - 132
2
b= 1 - 3, - 1021 - 10, - 132
1 4, - 72
1 6, 0 2. 1 0, 4 2.
x= 6 y= 42 x= 12 3 y= 122 x+ 3102 = 12 2102 + 3 y= 122 x+ 3 y=12.QUICK REVIEW
CONCEPTS EXAMPLES
3.2 The Slope of a Line
If then
slope mrise
runchange in y
change in x¢y
¢xy 2 y 1
x 2 x 1.
x 2 Zx 1 ,Find the slope of the graph of
Use the intercepts and and the slope formula.The graph of the line has undefined slope.
The graph of the line has slope
The lines and are parallel—both have
.The lines and are perpendicular—their
slopes are negative reciprocals.m=-1
3
y=-1
3
x+4
3
m= 3 3 y=-x+ 4y= 3 x- 1 x+ 3 y= 4y= 3 x- 1 x+ 3 y= 4m= 2y= 2 x- 3m= 2 - 2 y=- 4 x+ 6y= 2 x+ 3 4 x- 2 y= 6m= 2y= 2 x+ 3 4 x- 2 y= 6y=- 5 m=0.x= 3m= x 1 =6,y 1 =0,x 2 =0,y 2 = 44 - 0
0 - 6
=
4
- 6
=-
2
3
1 6, 0 2 1 0, 4 2
2 x+ 3 y=12.A vertical line has undefined slope.
A horizontal line has 0 slope.
Parallel lines have equal slopes.
The slopes of perpendicular lines, neither of which is
vertical, are negative reciprocals with a product of - 1.
(continued)