2.1
LINEAR EQUATIONS IN TWO VARIABLES (LINES AND SLOPES)
Formula for the Slope of a Line:
Change in y y y 2  y1


Change in x x x2  x1
Summary of Equations of Lines
1.
2.
3.
4.
5.
Point-Slope Form:
Slope-Intercept Form:
Horizontal Form:
Vertical Form:
Standard Form:
y  y1  mx  x1 
y  mx  b
ya
xb
Ax  By  C where A, B, C are integers
Steps for graphing y  mx  b :
1. Plot the y-intercept on the y-axis. This is the point (0, b).
2. Obtain a second point using the slope, m. Write m as a fraction, and use rise over run,
starting at the y-intercept.
3. Use a straightedge to draw a line through the two points. Draw arrowheads at the ends of
the line to show that the line continues indefinitely in both directions.
Slope and Parallel Lines:
1. If two lines are parallel, then they have the same slope.
2. If two different lines have the same slope, then they are parallel.
3. If two different lines are vertical (and therefore have undefined slopes), then they
are parallel.
Slope and Perpendicular Lines:
1. If two lines are perpendicular, then their slopes are negative reciprocals of each
other.
2. If two lines have slopes that are negative reciprocals of each other, then they are
perpendicular.
3. A horizontal line (having a slope of zero) and a vertical line (having an undefined
slope) are perpendicular.
Example 1
a)
b)
c)
d)
e)
f)
Sketch the graph of each linear equation.
y  x  2
1
y  x3
3
4x  y  4
y  2x  0
y  5
x5
Example 2
Find the slope of the line that contains the points given below.
 2, 0 and 3,1
 1, 2 and 2, 2
0, 4 and 1,  1
3, 4 and 3,1
a)
b)
c)
d)
Example 3
Find the slope of the vertical line that passes through the point  1, 4 .
Example 4
Find the equation of the linear function whose graph is given below.
8
6
4
2
-10
-5
5
10
-2
-4
-6
-8
Example 5
Graph the line that passes through the point  3,  3 with slope 0.
Example 6
Graph the line that passes through the point  2,  6 with slope
Example 7
Graph a line that has slope 5.
Example 8
Find the slope-intercept form of the equation of the line that has a slope of 3 and passes
through the point 1,  2 .
Example 9
a)
b)
5
.
3
Find the slope-intercept form of the equation of the line that pass through 2,  1 and is
parallel to the line with equation 2 x  3 y  5 .
perpendicular to the line with equation 2 x  3 y  5 .
Group Work Problem 1
Match each line with its corresponding equation below:
___ y  2 x
___ y  3
1
___ y   x  3
2
___ y 
___ y  2 x  3
___ y  3x
___ y 
1
x
4
1
x
2
Group Work Problem 2
Match the lines in the graph to the functions listed below.
____ y  x
____ y 
1
x2
10
____ y  3x
____ y  
____ y  3 x  4
1
____ y   x  2
2
1
____ y   x
2
____ y 
1
x
4
____ y 
1
x2
4
____ y  3 x
1
x2
10