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https://content-eu-central-1.knowunity.com/CONTENT/HxVCoPwvrustrVLqulLB.pdf

Study note

Shaivi Ramisetti

United States of America

DEFAULT (US)

Arithmetic

Slopes

Proportions

Graphs of proportional relationships

Slope
Slope the rate of change between any 2 points on a line
(the steepness of a line)
y
-8-
-7-
-6-
87654321
·3+∞-
-2
-1-
asu
slope
Slope
Lesson 1.8
run
change in y
change in x
1 2 3 4 5 6 7 8 x
- vertical change
-horizontal change
rise
run
||
3
2 Real
Example
1. The table below shows the relationship between the number of
seconds y it takes to hear thunder after a lightning strike and
the miles x you are from the lightning. Graph the data and find
the slope. Explain what the slope represents.
Miles (x)
0
Seconds (y) 0 5 10 15
Step 1: Graph the ordered pairs
from the table.
(x, y)
Seconds
b) Count the rise (up/down) and
the run (across) to make
the fraction. Simplify if
possible.
30
25
20
15
10
5
rise
run
20
ty
25
Step 2: Find the slope.
Method 1- Count Rise & Run on Graph
a) Draw a right triangle between 2 points on the line (make sure your
triangle follows the grid lines).
TE
an
0 1 2 3 4 5 6
Miles
2
10 2
5
X Method 2-Use Slope Formula
slope=
change in y
change in x
a) Choose any 2 points on the graph
and write the ordered pairs.
Label each coordinate.
b) Substitute each coordinate into
the formula. Solve and simplify.
=
Y2 - Y₁
X2
XI
(3, 15) and ( 5 , 25 )
X1 Yı
X2 Y2
=
||
||
=
Y2
X2 XI
25 - 15
5
3
10
12 51
slope
=
5
seconds
- miles
or 5
Step 3: Explain the slope's meaning.
For every 5 seconds between a lightening flash and the sound of
thunder, there is 1 mile between you and the strike. A.
Got It? Do this problem to find out.
Graph the data about plant height for a science fair project.
Then find the slope of the line. Explain what the slope
represents in the work zone.
X
Week
Step 1: Graph the ordered pairs
from the table.
Step 2: Find the slope.
rise
run
:
elw
-
2
Plant Height (cm)
Step 3: Explain the slope's meaning.
8965 & M N
7
y
(2,3) (46)
X₁ Y₁
Xa Ya
1
2
3
4
*B
:
+2
Y2-Y₁ 6-3
X2-X₁
4-2
X
0 1 2 3 4 5 6 7
Time (weeks)
Y
Plant Height
(cm)
1.5
3
4.5
6
6
10 دو
2
The plant grows 1.5 cm each week.
- The plant grows
3 cm
every
2 weeks. B. The table at the right shows the number of small packs of
fruit snacks y per box x. Graph the data. Then find the slope
of the line. Explain what the slope represents.
Step 1: Graph the ordered pairs
from the table.
Step 2: Find the slope.
8
rise
run
7
14
Number of Packs
Step 3: Explain the slope's meaning.
Ya-yı
ха-х,
28
24
20
16
12
8
41
OV
y
C
Boxes, x
Fruit
Snacks, y
+8
+2
(3,12) (5,20)
хауа
X, Y₁
357
12 20 28
1 2 3 4 5 6 7 X
Number of Boxes
5-3
20-123-4
There are 4 packs for each box. Real
Example
2. Renaldo opened a savings account.
Each week he deposits $300. Draw
a graph of the the account balance
versus time. Find the numerical
value of the slope and interpret it
in words.
Step 1: Graph the slope or
constant rate of change
given in the problem.
rise = $300
run = 1 week
initial value = 0
Amount ($)
2,400
1,800
1,200
600
0
y
Step 2: State the slope and explain its meaning.
300
2 4 6
Number of Weeks
Renaldo's account rises at a rate of $300 each week.
8 Got It? Do this problem to find out.
C. Jessica has a balance of $45 on her cell phone account.
She adds $10 each week for the next four weeks. In the work
zone, graph the account balance versus time. Find the
numerical value of the slope and interpret it in words.
Step 1: Graph the slope or
constant rate of change
given in the problem.
rise = 10
run = 1
initial value = 45
Account Balance ($)
80
60
40
20
y
X
1
2 3 4
Number of Weeks
Step 2: State the slope and explain its meaning.
Slope = 10
Jessica's account increases $10 each week.

Slopes

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Slopes

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

4.9+

13 M

#1

950 K+

Still not sure? Look at what your fellow peers are saying...

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

The application is very simple and well designed. So far I have found what I was looking for :D

Love this App ❤️, I use it basically all the time whenever I'm studying