module four lesson 2 remediation notes - slope intercept form
TRANSCRIPT
Slope-Intercept Form
y=mx + b
Slope
Recall the three methods we can use to find slope.
bmxyxxyym
runrisem
12
12
Slope
And recall the 4 types of slope
Positive Slope Negative Slope No Slope 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.
bmxyxxyym
runrisem
12
12
Remember this guy?
This is Slope Intercept Form.
We can use this equation to find the slope of a line and the y-intercept.
bmxy Remember this guy?
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.
initial
…a yearevery
each …a monthper
…a day
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.
initial originalstartingwhere x = 0 (flat) feeone time cost of one item
You Try!
xy 4
623
xy
8 xy
5 xy
Find the slope and y-intercept for the following equations
xy 4
623
xy
8 xy
5 xy
0int,4 ym
6int,23
ym
8int,1 ym
5int,1 ym
How did you do?
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
You can graph the line by following these simple steps:
1)Plot the y-intercept.
Notice that the slope is negative so the line must run from upper left to lower right!
(0,2)
(1,-1)
When given an equation like y = -3x + 2
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
Notice that the slope is negative so the line must run from upper left to lower right!
(0,2)
When given an equation like y = -3x + 2
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 3/13)Connect the points with a line.
(1,-1)
(0,2)
Notice that the slope is negative so the line must run from upper left to lower right!
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 isy = mx + b.
32 xy
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.
145
145
21238
212)3(8
m
Write the equation of the line in slope-intercept form that passes through the point (9,-2) and is
a)Parallel to y = -4x+7b)Perpendicular to y = -4x+7
Parallel Perpendicular
1. Slope of the parallel is -42. m = -4 and (9,-2)
1. Slope of the perpendicular is ¼ .
2. m = ¼ and (9,-2)
bbb
bmxy
34 362
)9)(4(2
b
bb
b
b
b
bmxy
417
417 498
449424
492
)9(412
344 xy4
1741 xy
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.
3. Use the values to find the equation.
(Let’s practice with point-slope formula this time)
The number picked depends on the time spent picking.
Number is dependent on time, so the ordered pairs will look like: (t, n)
(17, 26) and (85, 138)
1728
68112
851713826
m
m
m
21728
28172826
17172826
)1(1
xy
xy
xy
xxmyy
So, what does this mean?(let’s “interpret” a look on the next slide)
21728
xy
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
1. Independent and Dependent VariablesThe number picked depends on the time spent picking.
Number is dependent on time, so the ordered pairs will look like: (t, n) minutesin change
esstrawberri of #in change1728
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!