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Unit 2 Inequality Quiz
2( 3n + 7) > 5n
-3 (3x + 5) > -5 (2x – 2)
Writing Equations of a Line
Y=
mX + b
Graph y = 1/2 x -2
Steps
1. Plot 1st point on Y- intercept
2. Plot slope from 1st point
3. connect points with ruler
4. sign line at end
X Intercept =
Y Intercept =
m = slope of line
b = y intercept/ starting point
(X,Y) = coordinates
Writing Equations of a Line
Y=
mX + b
Y = 2/1 X -3
Steps
1. Plot 1st point on Y- intercept
2. Plot slope from 1st point
3. connect points with ruler
4. sign line at end
m = slope of line
b = y intercept/ starting point
(X,Y) = coordinates
How do we find slope without using a
Y2 - Y1
Slope= ______ ________
X2 - X1
coordinate plane?
Finding equation of a line with given slope
and 1 point
Y=mx+b
Slope = 2
(0,4)
Steps
1. Plug
given points into equation.
2. Solve
for b.
3. Write
equation.
Slope = 1/2
(2,1)
1. Plug
given points into equation.
2. Solve
for b.
3. Write
equation.
Graph 6y < 6 x -12 Using
table of values.
X
y
X Intercept =
Y Intercept =
Test Point (0,0) and Shade
Graph -3y > 1 x +9
Using table of values.
X
y
X Intercept =
Y Intercept =
Test Point (0,0) and Shade
Graph y > 1/2 x -2 Using
a table of values.
X
y
X Intercept =
Y Intercept =
Graphing Inequalities
Translate into equation
1. Y = 1/2 x - 2
2. Fill in table of values
3. Graph line
4. Shade after testing point
How could we solve??
Is the point (3,5) on the line 3x + 2y = 1
Madeline spent 120 minutes working on an English essay. On Tuesday, she spent 20 minutes linger than on Monday, and on
Wednesday, she spent rwice as long as she did on Tuesday. How many minutes did she spend working on the essay each
day if she finished on Wednesday?
Given 2 points graph a linear equation
xyxy
(1, 3) (3,4)
Steps:
1. Find Slope
m=
Y2 - Y1
Slope = ______ ________
X2 - X1
2. Sub 1 point and slope into equation.
3. Solve for b
b=
4. Rewrite equation in proper form.
5. Graph
Y= mx + b
Graph y = 1/2 x -2
Plot
x
Graph
2y -6 = 4x
x
Plot
y
y
Write in slope-intercept form.
x+
y = 12 4x -3y = 0
m= m=
b=
b=
Finding equation of a line with given slope and 1 point
Slope = 2 (0, 4)
Steps
1. Plug
given points into equation.
2. Solve
for b.
Given 2 points graph a linear equation
xyxy
(1, 3) (3,4)
Steps:
1. Find Slope
m=
Y2 - Y1
Slope = ______ ________
X2 - X1
2. Sub 1 point and slope into equation.
3. Solve for b
b=
4. Rewrite equation in proper form.
5. Graph
Graph the Equation
y - 6 = 3( x - 4)
y + 1 = 2( x - 5)
x
1
2
3
4
y
2
4
6
8
Formal Definition of a Function
A function relates each element of a set with exactly one element of another
set(possibly the same set).
X Does
Not Repeat
x
1
2
2
4
Domain = X
Range=Y
y
2
4
6
8
Write coordinates of each point listed
A
B
C
D
E
A
C
E
B
D
Quadrants
2
1
3
4
State type of slope
1.
2.
3.
3
4.
2
1
4
http://kutasoftware.com/FreeWorksheets/Alg1Worksheets/Slope%20From%20a% 20Graph.pdf
Find slope of line passing through given points.
(-4,1) and (3,4)
Steps
1.Plot points
2.Count rise over run
M
=
Rise
Run
Find slope of line passing through given points.
(1,1) and (3,-4)
Finding Slope from an Equation
Steps
1. Put equation in proper Y= MX +B form
2. Identify slope
M = Slope
B = Y intercept or Starting Point
y = − 5 /2 x − 5
2x − y = 1
y = −4x − 1
−2y − 10 + 2x = 0
Finding slope from an equation
http://kutasoftware.com/FreeWorksheets/Alg1Worksheets/Slope%20From%20an% 20Equation.pdf
Finding Slope without using a Graph
M=
Y2 - Y1
______
Steps
1. Substitute Coordinates into
slope formula.
2. Solve for M. (slope)
X2 - X1
X,Y X,Y
( 2 ,3 ) ( 4, 4)
X,Y X,Y
( -2 ,3 ) (4, -4)
X,Y X,Y
(-27,36) (14, -47)
http://kutasoftware.com/FreeWorksheets/Alg1Worksheets/Slope%20From%20Two% 20Points.pdf
Graph the given line
Y= 2x - 3
Make table for given line
X
Y
Determine if the given point is on the given line:
Y= 2X + 2
X
(1,4)
Steps
1. Put equation in Y=mx+b form
2. Graph on coordinate plane
3. Check points
r
1. Plug equation into calculator
o
2. Check points on table
Or
1. Substitute Values of X and Y into
2. Simplitfy Equation
3. Are both sides equal?
equation
Y
Determine if the given point is on the given line:
x = -4Y + 9 (1,2)
Steps
1. Put equation in Y=mx+b form
2. Graph on coordinate plane
3. Check points
or
1. Plug equation into calculator
2. Check points on table
X
Y
Evaluate f(x)
Given
f(x) = 3x-2
1. f (-3)
2. g (6)
and
g(x) = 1/2 x + 7, evaluate:
Bonus
24 X + 8 + 10X = -2 (4 + 7X)