3.2 Slope of a Line 1310 Fall 2011
Compare Lines with Different Slopes
The slope (m) of a line indicates how quickly the y-value changes as x-value increases.
Pick two distinct points (x1,y1) (x2,y2) on line
The slop formula m 
y2  y1
x2  x1
computes the slope
negative `
down left to right \
positive
up left to right
⁄
__
zero
horizontal
undefined
vertical
|
You may use either point as point 1 or point 2 (just not the same)
If you are given the equation of the line, you can determine the slope by solving for y. y = mx + b
The coefficient of x ( m ) is the value of the slope.
Note: There are occasions when the value of x1 and x2 are the same (vertical line). In this case the slope
is undefined (divide by 0 )
Determine if the graph increases or decreases
[12]
y = -4x + 2
[x1]
-x + 2y = -6
[x2]
x+y = x+3
[x3]
x+3 = 4
Vertical and Horizontal Lines
Vertical lines have a slope that is undefined.
(Note: The x-values of any two points on a vertical line are equal - divide by zero )
Horizontal lines have a slope equal to zero.
(Note: The y-values of any two points on a horizontal line are equal.)
General Form of a Linear Equation
Ax + By = C
Example: 4x – y = 2
A = 4, B = -1, C = 2
Example:
3x
+ 2 = 2( 3x – 2 ) + 2x - 3y
3x
+ 2 = 6x - 4 + 2x - 3y
3x
+ 2 = 8x - 3y - 4
-8x + 3y
-8x + 3y
-5x + 3y + 2 =
-4
.
-2
-2
-5x + 3y
=
-6
A = -5, B = +3, C = -6
Graph Equations in Slope-Intercept Form
Slope Intercept form: y = mx + b
m is the slope
b is the y-intercept ( 0, b )
Graph:
[22] y = -2x + 3
Determine Slope and y-intercept, then graph
[36] 5x + 3y = 6
Find the Slope-intercept Form Given Two Points on the Line
Compute the slope of the line using the slope formula m  y2  y1
x2  x1
Use either one of the points as (x1, y1) and the computed slope and put in x and y as the (x2, y2) point.
Solve for y.
Examples:
Find the slope and y-intercept of the lines thru
[44]
( 1, 7 ) and ( 3, 1 )
[50]
( 8, 2 ) and ( 8, -5 )
[52]
( -5, -1 ) and ( -3, -1 )