2. Using Slope
Linear Equation in Two Variable
Also know as slope-intercept form
y=mx+b
m = slope, b = y-intercept
Slope
Number of units the line rises (or falls) vertically
for each unit of horizontal change from left to
right
3. Slope-Intercept Form of the
Equation of a Line
Y=mx+b
Graphing a Linear Equation
Y = 2x + 1 m=2 b=1
Since b equals 1, y-intercept is (0, 1)
Since m = 2, line rises 2 units and moves over to the
right one unit 2/1
4. Finding the Slope of a Line
y2 - y1 = the change in y = rise
x2 - x1 = the change in x = run
(x1, y1) and (x2, y2) y2 y1
x2 x1
The Slope of a Line Passing Through Two Points
Slope m of the nonvertical line through
( x1, y1) and (x2, y2) is y 2 y1
x2 x1
5. Writing Linear Equations in
Two Variables
Point-slope form
y – y1 = m ( x – x1 )
Ex:
Using the point-slope form with m=3 and
(x1 , y1) = (1 , -2)
y – y1 = m ( x – x1)
y–(-2)=3(x–1)
y + 2 = 3x – 3
y = 3x – 5 This is written in slope-intercept form
6. Parallel and Perpendicular
Line
1. Two distinct nonvertical lines are parallel if
and only if their slopes are equal. That is,
m1 = m2
2. Two nonvertical lines are perpendicular if
and only if their slopes are negative
reciprocals of each other. That is, m1 = -1/ m2
7. Finding Parallel and
Perpendicular Lines
Find slope of a line that passes through the
point ( 2 , -1 ) and is parallel to line
2x – 3y = 5 or y = 2/3x – 5/3
Find a parallel line
Y – ( -1 ) = 2/3 ( x – 2 )
3(y+10=2(x–2)
3y + 3 = 2x – 4
Y = 2/3x – 7/3
8. Applications
Slope of a line can be interpreted as either a
ratio or a rate
If the x-axis and y-axis have the same unit of
measure, then the slope has no units and is a
ratio
If the x-axis and y-axis have different units of
measure, then the slope is a rate or rate of
change
