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Alg. 2, 2-2: Linear Relations and Functions
Presentation
•
Mathematics
•
10th - 12th Grade
•
Practice Problem
•
Medium
Standards-aligned
Jeremy Adelmann
Used 7+ times
FREE Resource
12 Slides • 15 Questions
1
Alg. 2, 2-2: Linear Relations and Functions
by Jeremy Adelmann
2
Multiple Select
Vocabulary: Please Take Notes
Linear Relations: relations that have straight line graphs
Linear Relations: relations that have straight line graphs
Linear Relations: relations that have straight line graphs
3
Multiple Select
Vocabulary: Please Take Notes
Linear Function: a function with ordered pairs that satisfy a linear equation. Can be written in the form f(x)=mx+b where m and b are real numbers.
Linear Function: a function with ordered pairs that satisfy a linear equation. Can be written in the form f(x)=mx+b where m and b are real numbers.
Linear Function: a function with ordered pairs that satisfy a linear equation. Can be written in the form f(x)=mx+b where m and b are real numbers.
4
Multiple Select
Vocabulary: Please Take Notes
Nonlinear relations: relations that are not linear
Nonlinear relations: relations that are not linear
Nonlinear relations: relations that are not linear
5
Multiple Select
Vocabulary: Please Take Notes
Linear equation: an equation with no other operations other than addition, subtraction, and multiplication of a variable by a constant. Variables CANNOT be multiplied together or appear in the denominator and cannot have exponents other than 1. The graph is always a line.
Linear equation: an equation with no other operations other than addition, subtraction, and multiplication of a variable by a constant. Variables CANNOT be multiplied together or appear in the denominator and cannot have exponents other than 1. The graph is always a line.
Linear equation: an equation with no other operations other than addition, subtraction, and multiplication of a variable by a constant. Variables CANNOT be multiplied together or appear in the denominator and cannot have exponents other than 1. The graph is always a line.
6
Identify Linear Functions
State whether each function is a linear function.
A.
This is a function because because it can be rewtitten into the slope intercept form of a line, f(x) = mx + b.
7
Identify Linear Functions
State whether each function is a linear function.
B.
This is NOT a function because because it cannot be rewtitten into the slope intercept form of a line, f(x) = mx + b.
It cannot be a function when the variable is the denominator of a fraction.
8
Identify Linear Functions
State whether each function is a linear function.
C.
This is NOT a function because because it cannot be rewtitten into the slope intercept form of a line, f(x) = mx + b.
It cannot be a function when there are more than one variable.
9
Multiple Choice
State whether each equation or function is a linear function. Explain.
3y−4x=20
Yes; it can written in the form f(x)=mx+b .
No; the variable is in the denominator of a fraction.
No; it has exponent other than 1.
No; the variable is under a square root.
10
Multiple Choice
State whether each equation or function is a linear function. Explain.
y=x2−6
Yes; it can written in the form f(x)=mx+b .
No; the variable is in the denominator of a fraction.
No; it has exponent other than 1.
No; the variable is under a square root.
11
Multiple Choice
State whether each equation or function is a linear function. Explain.
h(x) =6
Yes; it can written in the form f(x)=mx+b .
No; the variable is in the denominator of a fraction.
No; it has exponent other than 1.
No; the variable is under a square root.
12
Multiple Choice
State whether each equation or function is a linear function. Explain.
j(x)=2x2+4x + 1
Yes; it can written in the form f(x)=mx+b .
No; the variable is in the denominator of a fraction.
No; it has exponent other than 1.
No; the variable is under a square root.
13
Multiple Choice
State whether each equation or function is a linear function. Explain.
g(x)=5+x6
Yes; it can written in the form f(x)=mx+b .
No; the variable is in the denominator of a fraction.
No; it has exponent other than 1.
No; the variable is under a square root.
14
Multiple Choice
State whether each equation or function is a linear function. Explain.
f(x)=7+x
Yes; it can written in the form f(x)=mx+b .
No; the variable is in the denominator of a fraction.
No; it has exponent other than 1.
No; the variable is under a square root.
15
Standard Form of a Linear Equation
The standard form of a linear equation is Ax + By = C, when...
A, B and C are intergers with a GCF of 1,
A is greater than or equal to zero, and
A and B cannot both be zero.
Example:
16
Standard Form of a Linear Equation
Write each equation in standard form.
Subtract 4x from both sides.
Combine like terms.
17
Standard Form of a Linear Equation
Write each equation in standard form.
Subtract 4x from both sides.
Combine like terms.
Put into correct order
Multiply both side by -1 to
make the A value positive
In Standard Form
18
Standard Form of a Linear Equation
Write each equation in standard form.
Add 9 to both sides.
Combine like terms.
Divide both side by GCF, 3.
In Standard Form
19
Fill in the Blanks
Type answer...
20
Fill in the Blanks
Type answer...
21
Fill in the Blanks
Type answer...
22
x - and y - intercepts
X-intercept:
The x coordinate of the point at which the graph crosses the x-axis
The y coordinate will be zero. (x, 0)
Y-intercept:
The y coordinate of the point at which the graph crosses the y-axis
The x coordinate will be zero. (0, y)
23
Find the x and y Intercepts
Find the x- and y-intercepts of the graph 2x - 3y + 12 = 0.
Start by puttingin standard form.
Subtract 12 from both sides.
Simplify
24
Find the x and y Intercepts
Find the x- and y-intercepts of the graph 2x - 3y + 12 = 0.
A. Find the x-intercept
Let y = 0
Multiply
Simplify
Divide both sides by 2
The x-intercept is -6
25
Find the x and y Intercepts
Find the x- and y-intercepts of the graph 2x - 3y + 12 = 0.
B. Find the y-intercept
Let x = 0
Multiply
Simplify
Divide both sides by -3
The y-intercept is 4
26
Fill in the Blanks
Type answer...
27
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Type answer...
Alg. 2, 2-2: Linear Relations and Functions
by Jeremy Adelmann
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