what do you know about slope? 1.slope is represented by the constant in front of the independent...
TRANSCRIPT
What do you know about slope?
1. Slope is represented by the constant in front of the independent variable.
2. Slope is always written as a fraction.3. The slope in the formula 2y= 1/3 x +5 is “1/3”4. The slope in the formula 2y = 4x +6 is “4”5. Slope means run over rise.6. Slope only means rise over run.7. Counting rise over run is the easiest way to find
the slope of a line8. If the dependent variable in a function is 0 for all
numbers the resulting line is vertical9. If the independent variable in a function is the
same for all dependent variables the resulting number is a horizontal line
10.You only find slope when the equation is written in slope intercept form
Essen
tial Q
uestio
n: How
can y
ou d
escr
ibe
the
graph o
f the
equat
ion
y=m
x+b?
` OB
J EC
T I VE S :
1. F I ND
I NG
TH
E SLO
P E OF A
LI N
E
2. F I ND
I NG
TH
E SLO
P E OF A
LI N
E
F RO
M A
TA B
L E
3. I DEN
T I FY I N
G S
LOP E S A
ND
Y-
I NT E RC
E P T S
4. US I N
G S
LOP E - I
NT E RC
E P T FO
RM
TO
GRA PH
LI N
E AR E
QU
AT I ON
S
Vocabulary:
SLOPE: • The rate of change between any two points on a line.• The measure of the steepness of a line
To find the slope of a line, find the ration of the change in y (the vertical change – rise) to the change in x (the horizontal change – run)
Slope =Change in yChange in x
=Y2 – Y1
X2 – X1
Fun fact: Renee Decartes was a French mathematician, physicist, philosopher, and theologian. Many mathematics experts acknowledge him as the man who discovered the slope formula.
Constant function: a linear function of the form y=b & has a slope of 0
Objective #1: Find the slope of a LineExamples:
The line rises from left to right so the slope is positiveLet (X1,Y1) = (-3,-2) and let (X2,Y2) = (3,2)
The line falls from left to right so the slope is negativeLet (X1,Y1) = (0,2) and let (X2,Y2) = (2,-1)
m=Y2 – Y1
X2 – X1
=2 – (-2)
3 – (-3)
=4
6 =
2
3 m=
Y2 – Y1
X2 – X1
=-1 – 2
2 – (0) =
-32
Write a left column question about Objective #1
Objective #2: Find the slope from a table
x f(x)
4 20
7 14
10 8
13 2
x f(x)
-1 2
1 2
3 2
5 2
x f(x)
-3 -3
-3 0
-3 6
-3 9
Choose any two points from table a.Use the points in the slope formulaLet (X1,Y1) = (4,20) and let (X2,Y2) = (10,8)
m=Y2 – Y1
X2 – X1
=8 –20
10 – 4 =
-12
6 =
-21
a. b. c.
Choose any two points from table b.Use the points in the slope formulaLet (X1,Y1) = (3,2) and let (X2,Y2) = (5,2)
m=Y2 – Y1
X2 – X1
=2 – 2
5 – 3 =
0
2
Choose any two points from table c.Use the points in the slope formulaLet (X1,Y1) = (-3,-3) and let (X2,Y2) = (-3,6)
m=Y2 – Y1
X2 – X1
=6 – (-3)
-3 – (-3)
=9
0 or undefined
or 0
Objective #2: Finding slope from a table (continued)
Positive Slope:
The line rises from left to right
Negative Slope:
The line falls from left to right
Slope of 0: The line is horizontal(constant function)
Undefined Slope:
The line is vertical
Write a left column question about Objective #2
Objective #3: Identifying slopes and Y-intercepts
Slope-Intercept form
Isolate y
Write a left column question about Objective #3
y = m x + b
slope
y-- intercept
Rewrite into Slope-Intercept form
Standard form
1) -4x + y = -4
2) 3x + y = 5
3) -9x - 3y = 6
Re-write each standard form equation in slope-intercept form:
y = 4x – 4 y = - 3x + 5 y = -3x + 2
Objective #4: Using Slope-intercept form to graph linear equations
Graph: 2x + y = 2Re-write in slope-intercept formy = - 2x + 2
y = -2 (0) +2
Find the y intercept
Graph the y intercepts and use the slope to graph the next point
(0 , 2)
m = -2 and b = 2
Find the slope and the y intercept
x
y
1 2
1
2
- 2
1
Objective #4: Using Slope-intercept form to graph linear equations (continued)
Graphing from a verbal description:
Write a left column question about Objective #4
A linear function g(x) models a relationship in which the dependent variable increases 3 units for every 1 unit the independent variable increases. Graph g(x) when g(0) =3Identify: The slope, the y intercept and the x intercept. Graph the g(x)
x
y
-2
2
-4
4
Slope:Change in y
Change in x
Dependent increases 3Independent increases 1
m=3
1
y intercept: g(x)=mx+b or g(0)= 3(0) + 3 = g(0)=3 (0,3)x intercept: g(x)=mx+b or 0 = 3x + 3 = -3=3x = -1=x (-1,0)
What do you now know about slope?
1. Slope is represented by the constant in front of the independent variable. -True
2. Slope is always written as a fraction. - False3. The slope in the formula 2y= 1/3 x +5 is “1/3” - False4. The slope in the formula 2y = 4x +6 is “4” - False5. Slope means run over rise. – False 6. Slope only means rise over run. - False7. Counting rise over run is the easiest way to find the
slope of a line - False8. If the independent variable in a function is 0 for all
numbers the resulting line is vertical - False9. If the dependent variable in a function is the same for all
y numbers the resulting number is a horizontal line - False
10.You only find slope when the equation is written slope intercept form - FalseWrite a summary of what you have learned
about slopes …