Unit 2Linear Equations and Functions

Unit Essential Question:

What are the different ways we can graph a linear equation?

Lessons 2.1-2.3Functions, Slope, and Graphing Lines

What is a function?

Domain Range

Rate of Change = Slope

𝑚=h𝑐 𝑎𝑛𝑔𝑒𝑖𝑛𝑦 𝑣𝑎𝑙𝑢𝑒𝑠change∈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 that passes through the point (-2,1).

2) Write the equation of a line in standard form that is perpendicular to the line that passes through the point (-4,8)

Lesson 2.4 – 2.6Parallel/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 2.7Absolute 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 the function:

This is the parent function for absolute value functions.

Examples: Create a table of points, to determine the graph of

the given functions.

Ex:

Ex:

Ex:

Ex:

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

1)

2)

3)

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