Find the slope of a line. Write the equation of a line.

1. Slopes and Equations of Lines
The student is able to (I can):
• Find the slope of a line given
— Graph
— Two points
— Equation
• Write the equation of a line given
— Slope and y-intercept
— Slope and point on line
— Two points
— Graph

2. rise
run
The difference in the yyyy----valuesvaluesvaluesvalues of two points
on a line.
The difference in the xxxx----valuesvaluesvaluesvalues of two points
on a line.
2 4 6 8
-2
2
4
6
8
x
y
•
•(xxxx1111, yyyy1111)
(xxxx2222, yyyy2222)
run = 4run = 4run = 4run = 4
rise = 6rise = 6rise = 6rise = 6

3. slope The ratio of riseriseriserise to runrunrunrun. If (xxxx1111, yyyy1111) and
(xxxx2222, yyyy2222) are any two points on a line, the
slope of the line is
So, for the previous example, substitute
(1111, 1111) for (xxxx1111, yyyy1111) and (5555, 7777) for (xxxx2222, yyyy2222):
Note: Always reduce fractions to their
simplest forms. Also, it’s usually better to
leave improper fractions improper.
2 1
2 1x
y
m
y
x
−
−
=
1
2 1
2
x x
y y 7 6 3
m
41 2
1
5
− −
= = = =
− −

4. Summary: Slope of a Line
positive slope negative slope
zero slope undefined slope

5. Practice
Find the slopes between the following points:
1. (2, —1) and (8, —4) 2. (—3, 10) and (5, —6)
3. (1, 12) and (—10, —10) 4. (22, 4) and (0, 28)
( )− − − −
= = = −
−
4 1 3 1
m
8 2 6 2 ( )
− − −
= = = −
− −
6 10 16
m 2
5 3 8
− − −
= = =
− − −
10 12 22
m 2
10 1 11
−
= = = −
− −
28 4 24 12
m
0 22 22 11

6. Point-Slope
Form
Given the slope, mmmm, and a point on the line
(xxxx1111, yyyy1111), the equation of the line is
y — yyyy1111 = mmmm(x — xxxx1111)
Example: Write the equation of the line
whose slope is 2222, which goes through the
point (1111, 6666)
y — 6666 = 2222(x — 1111)
In point-slope form, you can leave it like this
— you don’t have to simplify it any
further.

7. Slope-
Intercept Form
Given the slope, mmmm, and bbbb, the y-intercept,
the equation of the line is
y = mmmmx + bbbb
Example: For mmmm = ————3333 and y-intercept 7777,
find the equation of the line.
y = ————3333x + 7777

8. Horizontal Line
Vertical Line
For a horizontal line (mmmm = 0000), the equation
of the line is
y = bbbb
For a vertical line (mmmm = undefinedundefinedundefinedundefined), the
equation of the line is
x = xxxx1111
Notice that this equation does not start
with “y=“

9. Practice
Write the equations in point-slope form
1. m = —2; (3, 5) 2. (1, 2)
y — 5 = —2(x — 3)
3. m = —4; (—1, 4) 4. (—2, —3)
y — 4= —4(x + 1)
Write the equations in slope-intercept form
5. m = 6, b = 2 6. m = —1, b = —4
y = 6x + 2 y = —x — 4
2
m ;
3
=
3
m ;
4
= −
2
y 2 (x 1)
3
− = −
3
y 3 (x 2)
4
+ = − +

10. Practice
7. Write the equation of the line through (————1111, 0000) and (1, 2) in
slope-intercept form.
2 0 2
m
1 ( 1) 2
1
−
= = =
− −
Method #1
y — 0000 = 1111(x + 1111)
y = x + 1
Method #2
0000 = (1111)(————1111) + b
0 = —1 + b
1 = b
y = x + 1