Download Slope

Slope-Intercept Form
y=mx + b
Slope
Recall the three methods we can use to find slope.
rise
m
run
y2  y1
m
x2  x1
y  mx  b
Slope
And recall the 4 types of slope
Positive Slope
Negative Slope
Slope of Zero
Undefined Slope
Increases Left to Right
Decreases Left to Right
Horizontal Line
Vertical Line
y = 3x + 2
y = - 3x + 2
y=3
x=5
Slope
There are 3 methods we can
use to find slope!
Each one works best
for certain situations.
Remember this guy?
rise
m
run
y2  y1
m
x2  x1
y  mx  b
Remember this guy?
y  mx  b
This is Slope Intercept Form.
We can use this equation to
find the slope of a line and the
y-intercept.
The slope is a constant but it
is always affected by something.
The slope tells you the rate of change over each interval or
time or an occurrence.
The y-intercept is a constant.
This means that it is the starting point in a word problem, or a
value that does not change and is not affected by anything
happening within the word problem.
You Try!
Find the slope and y-intercept for the following equations
y  4x
3
y  x6
2
y  x  8
y
x5
How did you do?
y  4x
m  4, y  int  0
3
y  x6
2
3
m  , y  int  6
2
y  x  8
m  1, y  int  8
y
x5
m  1, y  int  5
Graphing
When given an equation like
y = -3x + 2
You can graph the line by
following these simple steps:
When given an equation like
y = -3x + 2
You can graph the line by
following these simple steps:
1) Plot the y-intercept.
(0,2)
When given an equation like
y = -3x + 2
Notice that the slope is
negative so the line
must run from upper
left to lower right!
You can graph the line by
following these simple steps:
1) Plot the y-intercept.
(0,2)
When given an equation like
y = -3x + 2
Notice that the slope is
negative so the line
must run from upper
left to lower right!
You can graph the line by
following these simple steps:
1) Plot the y-intercept.
2) Use the slope to trace
(rise / run) to the next
point on the line.
-3 is actually - 3/1
(0,2)
(1,-1)
When given an equation like
y = -3x + 2
Notice that the slope is
negative so the line
must run from upper
left to lower right!
You can graph the line by
following these simple steps:
1) Plot the y-intercept.
2) Use the slope to trace
(rise / run) to the next
point on the line.
3 is actually 3/1
3) Connect the points with
a line.
(0,2)
(1,-1)
Review Problems
Given:The slope of a line is -2 and the y-intercept is 3.
Write the equation of the line in slope-intercept form.
The information provided is enough for you to write the
equation. m = -2, b = 3 and slope-intercept form is
y = mx + b.
y  2 x  3
Write the equation of the line in slope-intercept form
that passes through the points: (2,-3) and (-12,-8).
To write an equation in slope-intercept form we need the
slope.
1. Use the ordered pairs to find the slope.
 8  (3)  8  3
5
5
m



 12  2
 12  2  14 14
Write the equation of the line in slope-intercept form
that passes through the point (9,-2) and is
a) Parallel to y = -4x+7
b) Perpendicular to y = -4x+7
Parallel
1. Slope of the parallel is
2. m = -4 and (9,-2)
Perpendicular
-4
1. Slope of the perpendicular is
¼.
2. m = ¼ and (9,-2)
y  mx  b
y  mx  b
1
 2   (9)  b
4
9
2  b
4
 2  (4)(9)  b
 2  36  b
34  b
4 2  4 9   4b 
4
 8  9  4b
y  4 x  34
1
17
y  x
4
4
 17  4b

17
b
4
Celia is out picking strawberries. She had 26 strawberries in her bucket
after she had been picking for 17 minutes. She is now finished after
spending 85 minutes picking. She has 138 strawberries.
Write an equation to model the number of strawberries, n, Celia picked per
minute, t.
1. Independent
and Dependent
Variables
2. After you
write the
ordered pairs,
find m.
The number
picked depends
on the time
spent picking.
(17, 26) and
(85, 138)
Number is
dependent on
time, so the
ordered pairs will
look like:
(t, n)
26  138
17  85
 112
m
 68
28
m
17
m
3. Use the values to find the equation.
(Let’s practice with point-slope
formula this time)
y  y1  m( x  x1)
28
x  17 
17
28
y  26 
x  28
17
28
y
x2
17
So, what does this mean?
(let’s “interpret” a look on the next slide)
y  26 
1. Independent
and Dependent
Variables
The number
picked depends
on the time
spent picking.
Number is
dependent on
time, so the
ordered pairs will
look like:
(t, n)
We determined that the number of
strawberries she had depended on the amount
of time she had been picking.
The slope, 28/17, is the change in “y” or
dependent value, which is n in this case over the
change in “x” or the independent value, which
is t in this case.
So we can say that
28 change in # of strawberri es

17
change in minutes
28
y
x2
17

Interpret slope : for every 17 minutes she picked 28
strawberries.

Or, if we find the unit rate by dividing, we get 1.647,
which means for every 1 minute she picked about
1.647 strawberries.

Interpret y-intercept : she began with -2
strawberries. This is not realistic!