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Unit 2
Linear Equations and Functions
Unit Essential Question:

What are the different ways we can graph a linear equation?
Lessons 2.1-2.3
Functions, Slope, and Graphing Lines
What is a function?

Domain

Range
Rate of Change = Slope
𝑚
=
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦 𝑣𝑎𝑙𝑢𝑒𝑠
change in x values
Graphing Linear Equations

Slope Intercept Form

Standard Form

Horizontal

Vertical
Homework:
 Have
a good weekend!
Bell Work:

1) Write an equation of a line in standard form that is
parallel to the line 𝑦 = −4𝑥 + 2 that passes through the
point (-2,1).

2) Write the equation of a line in standard form that is
perpendicular to the line 4𝑥 − 2𝑦 = 10 that passes through
the point (-4,8)
Lesson 2.4 – 2.6
Parallel/Perpendicular Lines, Standard
Form, and Direct Variation
Parallel Lines

Lines that never intersect. If two lines never
intersect, then they must have the same…
SLOPE!!!!!!

The lines y = 3x + 10 and y = 3x – 2 are parallel!!!
Perpendicular Lines

Intersecting lines that form 90 degree angles.
Perpendicular lines have the opposite-reciprocal slope.

The lines y = 3x + 4 and y = -1/3x – 8 are perpendicular.
Standard Form

Ax + By = C, where A, B, and C are integers (not fractions
or decimals).

To graph a linear equation in standard form, find the x
and y intercepts.

X-intercept: this is when y = 0, so simply plug 0 in for y,
and solve for x.

Y-intercept: this is when x = 0, so simply plug 0 in for x,
and solve for y.
Direct Variation

In the form y = kx, where k is the constant of variation.

To find an equation in direct variation form, you use a
given point to find k.

Example: If y varies directly with x, and when x = 12, y =
-6, write and graph a direct variation equation.
Homework:

Page 102 #’s 20 – 25, 40 – 45

Page 109 #’s 3 – 29 odds
Bell Work:

1) Write the equation of a line in standard form
that passes through the point (6,-2) and is
perpendicular to the line y = -3x + 4.

2) If y varies directly with x, and when x = 10, y =
-30, write and graph a direct variation equation.
Lesson 2.7
Absolute Value Functions
Lesson Essential Question:

How do we graph an absolute value function, and how can we predict
translations based upon its equation?
Example:
 Graph
 This
the function: 𝑦 = |𝑥|
is the parent function for absolute
value functions.
Examples:

Create a table of points, to determine the graph of the
given functions.

Ex: 𝑦 = 𝑥 − 2

Ex: 𝑦 = 𝑥 + 3

Ex: 𝑦 = −2 𝑥 + 6

Ex: 𝑦 = 3 𝑥 − 2
Examples with Transformations:
Homework:

Page 127 #’s 3 – 20
Bell Work:

Explain what would happen to each function based upon
the changes to the original parent function 𝑦 = 𝑥 .

1) 𝑦 = 𝑥 − 5

2) 𝑦 = − 𝑥 + 5

3) 𝑦 = 𝑥 + 3 − 2
Stretching/Shrinking

When the absolute value function is multiplied by a number other than 1, it
causes the parent function to:

Stretch if the number is greater than 1.

Shrink if the number is between 0 and 1.
Transformations:

This is when a basic parent function is translated, reflected, stretched
or shrunk.

Translation: when it is shifted left, right, up, or down.

Reflection: when it is reflected across the focal point. (multiplied by
a negative)

Stretched: when it is vertically pulled (multiplied by a # > 1).

Shrunk: when it is vertically smushed (multiplied by a # between 0
and 1.
Examples:
Homework:

Page 127 #’s 3 – 20
Bell Work:

1) Write the equation of a line in standard form that passes through
the point (-2,6) and is parallel to the line 4x – 2y = 8.

2) Find the slope between these two points: (-30,10) and (-6,22)

3) If y varies directly with x, and when x = -3, y = - 21, write a direct
variation equation and then find y when x = 20.

4) Sketch the graph of 𝑦 = −4 𝑥 + 3 + 2