Geometry
• Agenda
1. ENTRANCE
2. Go over Practice
3. 3-5 Continued
4. Practice
5. EXIT
Practice
Chapter 3
3-5 Continued
Slope
• The steepness of a line
•
ryse
run
y2  y1
• m
x2  x1
( x2 , y2 )
( x1 , y1 )
Types of Slope
• Positive
• Negative
• Zero
• No
Equations of Lines
• A line is a set of points. Every line has an
equation that relates the coordinates of
these points.
ex:
2x - 3y = 14
(1, -4) (4, -2) (2.5, -3)
(-2, -6) (-0.5, -5) (7, 0)
Forms of a Line
• These are each different forms of the same
equation.
2x - 3y = 14
Standard form
2
14
y = x
3
3
Slope-Intercept form
2
y + 4 = (x -1)
3
Point-Slope form
Standard Form
• This equation is of the form Ax + By = C.
The x and y terms are on the left side and
the constant is on the right side of the
equation.
2x - 3y = 14
Slope-Intercept Form
• This equation is of the form y = mx + b.
The y term is on the left and the x term is
on the right side of the equation. The
value of m is the slope of the equation.
The value of b is the y-intercept.
2
14
y = x
3
3
Point-Slope Form
• This equation is of the form
y – y1 = m(x – x1).
The y term is on the left and the x term is on the right
side of the equation. The value of m is the slope of the
equation. The values x1 and y1
are the coordinates of a
point on the line.
2
y + 4 = (x – 1)
3
2
m=
(1, -4)
3
Example #1
• Graph.
2
y  x 1
3
Example #2
• Graph.
3x  2 y  6
Example #3
• Graph.
x  2y  4
Example #4
• Find the equation of a line with slope -3
that contains the point (-1, 4).
Example #5
• Find the equation of a line that contains
the points (6, 3) and (-4, 5).
Example #6
• Find the equation of a horizontal line
through the point (-3, 1).
Example #7
• Find the equation of a vertical line through
the point (1, -2).
Example #8
• A truck ramp is being redesigned for a
local moving company. What is the
equation of the line that represents the
ramp?
Example #9
• The equation P = $300m + $2000 represents the
total payment (P) after m number of months for
purchasing a car from the local dealership.
– What is the slope of the line represented by this
equation?
– What does the slope represent in this situation?
– What is the y-intercept of the line?
– What does the y-intercept represent in this situation?
• Practice
– WB 3-5 # 4, 8, 13, 14, 21, 27, 28, 36, 45, 46
• EXIT