Linear Functions and Slope

1
Section 1.3

• Linear Functions and Slope

2
Linear Functions
They can be written
f(x) m(x) b
Slope
y-intercept includes the sign
What happens if m0?
What happens if m1 and b0?
3
Special Linear Relations
Vertical lines
Horizontal lines
They have the equation xa
Have the equation f(x)b or yb
They are not functions
They are functions
4
Give the equations for the vertical and
horizontal lines through (6,4)
(6,4)
Y4
X6
5
Slope
Notice the vertical association for the pairs of
coordinates
6
Find the slope of the line passing through (9,4)
and (-1,2)
TI-84
Try (-3,7) and (5,-1)
7

• Hit Stat and the Edit on the menu that appears

If you cannot see list 1 and list 2, quit to the
main menu and hit stat, 5, enter Then go back
to step 1
2. If there is data in list 1 and/or list 2,
clear the data
To clear data, cursor up until the cursor is on
the list name, then hit clear and enter
3. Enter x coordinates one at a time in list 1,
hit enter to go to the next
4. Enter y coordinates one at a time in list 2,
hit enter to go to the next
5. Hit stat, over to calc, then down to 4,
hit enter
8
Get used to f(x) instead of y
y 3x 2
f(x) 3x 2
Find f(4)
We put in a 4 in the place of x
f(4) 3(4) 2
f(4) 14
What is y?
What is x?
9
Looking at points to find a function
We will use a scatter plot in TI-84 or by hand
x
y
11
3.2
26
5.7
41
8.2
56
9.3
71
11.3
86
13.7
101
19.1
10
f(x) m(x) b
Slope
y-intercept includes the sign
Give the slope and the y-intercept for the
following
f(x) 3x 2
f(x) -2x - 3
f(x) -2x 3
f(x) 3x - 2
11
Find the slope given
f(-4) -5 and f(4) 1
What does this tell us?
TI-84
12
Point slope gsp