1. 1.3 LINEAR EQUATIONS
IN TWO VARIABLES

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