1.4 Graphing Lines
If real is what you can feel, smell, taste, and see, then
“real” is simply electrical signals interpreted by the brain.
-Morpheus
Slope of a Line
y
y 2  y1
m
x 2  x1
P2 (x2, y2 )
P1(x1, y1)
y2  y1

x2  x1




x
x1  x 2
Slope of a Line
y
y 2  y1
m
x 2  x1
P2 (11,6)
P1(2,3)



x
x1  x 2
Slope of a Line
Find the slope of the line shown below.
Vertical and Horizontal Lines
Let’s take a look at the vertical line and horizontal line through
the point (-3,1).
Horizontal Lines
Slope = 0
Equation: y  b
Vertical Lines

Slope Undefined
Equation: x  a

Forms of a Line
Slope-Intercept Form: y  mx  b
m = slope b = y-intercept
1
Ex : y  x  3
2
 y  y1  m(x  x1)
Point-Slope Form:

1
Ex : y  3  (x  0)
2
m = slope (x1,y1) = point on line
1
Ex : y  2  (x  2)
2
General
Form: Ax  By  C

A,B are integers ≠ 0 and A > 0


Ex : x  2y  6

Forms of a Line - Practice
2
1) Write the equation of the line y  x  4 in general form.
3

1
2) Write the equation of the line (y  2)   (x 1) in slope2
intercept form.

Finding Equations From Graphs
Find the equation of the line. Write your answer in slopeintercept form.
Finding the Equation of a Line
Find an equation for the line with the given properties. Express
your answer in Slope-Intercept Form.
1) Slope = 2; containing the point (4,-3)
Finding the Equation of a Line
Find an equation for the line with the given properties. Express
your answer in General Form.
2) Containing the points (-3,4) and (2,5)
Finding the Equation of a Line
Find an equation for the line with the given properties.
3) Slope undefined containing the point (3,8)
Parallel and Perpendicular Lines
Parallel Lines have
slopes that are equal.
Perpendicular Lines
have slopes that are
opposite reciprocals.
Finding the Equation of a Line
Find an equation for the line with the given properties. Express
your answer in Slope-Intercept Form.
4) Parallel to the line 3x + y = 4; containing the point (-1,2)
Finding the Equation of a Line
Find an equation for the line with the given properties. Express
your answer in General Form.
5) Perpendicular to the line x - 2y = -5; containing the point (0,4)

Graphing Lines in General Form
When equations are in general form, we can use the intercepts
to help us graph without solving for y.
2x  4 y  8
More Practice…before you get your homework, k?
1) Find the slope of the line containing the points (-2,-1) and
(5,-6).
2) Find the slope and the y-intercept of the following lines.
3
b) (y  4)  (x  8)
4
a) 2x  5y  10
3) Find the equation of the line below in slope-intercept form.


1.4 Graphing Lines
Homework #14:
Graphing Worksheet
If real is what you can feel, smell, taste, and see, then
“real” is simply electrical signals interpreted by the brain.
-Morpheus