Download Linear Functions: Review of Slope and Intercept

Name:
Date:
Algebra 2
Linear Functions: Review of Slope and Intercept
This worksheet should be review for you. If you need more explanation, please see Chapter 2 in your
textbook and come for extra help.
A linear function is a function whose graph is a straight line. Every linear function has a number called its
slope. The slope m tells you the direction and the steepness of the line.
One common way to write a linear equation is in “slope-intercept” form:
f(x) = mx + b or y = mx + b, where the number m is the slope and the number b is the y-intercept.
Other ways to find slopes:
A. If you have a line graph, choose any two points on the line.
(It’s easiest if you choose points located at grid
intersections.)
rise
run
Count squares to find the rise and the run.
(If the rise goes down, use a negative number for the rise.)
rise
Then m =
.
run
B. Using any two points (x1, y1) and (x2, y2) taken from a table or a graph, you can also find the rise and
the run by subtracting:
rise y 2 - y1
.
m=
=
run x2 - x1
Example: Find the slope of the line through the points (3, –5) and (10, 4).
Solution: x1 = 3 y1 = –5 x2 = 10
4 - (-5) 9
slope = m =
= .
10 - 3
7
y2 = 4
C. If you have a table of values where the x-values go up by 1’s, the y-values go up or down by the slope.
Examples:
x
–3
–2
–1
0
1
2
3
y
–5
–3
–1
1
3
5
7
This table has a slope of 2.
x
–3
–2
–1
0
1
2
3
f(x)
5.0
4.5
4.0
3.5
3.0
2.5
2.0
This table has a slope of –0.5.
For tables where the x-values have a different spacing or an uneven spacing, just choose
any two points from the table and use method B instead.
D. IMPORTANT TO REMEMBER: Horizontal lines always have slope = 0. Vertical lines have no
slope.
Name:
Date:
Algebra 2
Problems
1. Write the equations for the following lines:
a.
b.
d.
g.
e.
c.
f.
h.
Name:
Date:
Algebra 2
2. Write the equation for the line passing through each pair of points specified. (Hint: Find the slope and
then plug in a point to find the y-intercept (“b”).)
a. (1, –2) and (4, –3)
c. (–3, 1) and (5, 1)
b. (–3,3) and (–4, 4)
d. (20, 100) and (80, 1000)
3. Each table represents a linear function. Write the equation for the function.
a.
b.
x
–3
–2
–1
0
1
2
3
y
8
5
2
–1
–4
–7
–10
c.
x
–3
–2
–1
0
1
2
3
f(x)
–2
–0.5
1
2.5
4
5.5
7
d.
x
–6
–4
–2
0
2
4
6
y
21
17
13
9
5
1
–3
x
–8
–5
–2
0
2
5
7
f(x)
–15
–9
–3
1
5
11
15
Name:
Date:
Algebra 2
4. Graph the equation y = – 12 x + 6.
5. Graph the equation f  x  
6. Graph the equation y = –x
3
x7
5
Name:
Date:
Algebra 2
ANSWERS:
1.
2.
a. f x  
b.
c.
d.
e.
2
x 1
3
2
f x    x  1
3
3
f x   x  1
2
1
f x   x  3
2
f x   2 x  3
1
f. f x    x  3
2
g. f  x    x
f. f x   4
a. f  x   5 x  9
b. f  x    x
c. f  x   1
d. f  x   15 x  200
3.
a. f x   3x  1
b. f x  
3
5
x
2
2
c. f x     2 x  12 x  9
d. f  x 
4.
5.
6.
.