unit 2 linear equations and functions. unit essential question: what are the different ways we can...
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Unit 2Linear Equations and Functions
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Unit Essential Question:
What are the different ways we can graph a linear equation?
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Lessons 2.1-2.3Functions, Slope, and Graphing Lines
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What is a function?
Domain Range
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Rate of Change = Slope
𝑚=h𝑐 𝑎𝑛𝑔𝑒𝑖𝑛𝑦 𝑣𝑎𝑙𝑢𝑒𝑠change∈x values
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Graphing Linear Equations
Slope Intercept Form Standard Form Horizontal Vertical
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Homework:
Have a good weekend!
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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)
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Lesson 2.4 – 2.6Parallel/Perpendicular Lines,
Standard Form, and Direct Variation
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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!!!
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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.
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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.
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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.
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Homework:
Page 102 #’s 20 – 25, 40 – 45
Page 109 #’s 3 – 29 odds
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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.
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Lesson 2.7Absolute Value Functions
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Lesson Essential Question:
How do we graph an absolute value function, and how can we predict translations based upon its equation?
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Example:
Graph the function:
This is the parent function for absolute value functions.
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Examples: Create a table of points, to determine the graph of
the given functions.
Ex:
Ex:
Ex:
Ex:
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Examples with Transformations:
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Homework:
Page 127 #’s 3 – 20
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Bell Work:
Explain what would happen to each function based upon the changes to the original parent function
1)
2)
3)
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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.
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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.
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Examples:
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Homework:
Page 127 #’s 3 – 20
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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