Equations of Parallel and Perpendicular Lines
Today you will need:
Grab a warm-up off the wooden desk and get started!
Goals:
Warm-up #1:
Solve the given equations for y.
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Warm-up #2
Recall: 3 forms of linear equations
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Which form(s) is/are easiest to graph from? Why?
What can you do if the equation isn’t given to you in that form?
What do you notice/wonder about these parallel lines? What makes them parallel? How do you know?
What do you notice/wonder about these perpendicular lines? What is “perpendicular”?
How can you tell from their equations that they are perpendicular?
Parallel & Perpendicular Line Equations
Parallel & Perpendicular Line Equations
Parallel & Perpendicular Line Equations
Parallel & Perpendicular Line Equations
Parallel & Perpendicular Line Equations
Parallel & Perpendicular Line Equations
Equations of Parallel and Perpendicular Lines
Today you will need:
Grab a warm-up off the wooden desk and get started!
Goals:
Find the slope of the line passing through the pairs of points and describe the line as rising, falling, horizontal or vertical.
(2, 1) and (4, 5) | (-1,0) and (3, -5) | (2, 1) and (-3, 1) | (-1, 2) and (-1, -5) |
Determine whether the graphs of each pair of equations are parallel, perpendicular or neither.
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Write the equation in slope-intercept form of the line that is parallel to the graph of each equation and passes through the given point.
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Write the equation in slope-intercept form of the line that is perpendicular to the graph of each equation and passes through the given point.
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Are the lines L1 and L2 passing through the given pairs of points
parallel, perpendicular, or neither parallel nor perpendicular?
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Log on to desmos
Practice Time!
Resources
Mod 1 Standards
N.Q.2 Define appropriate quantities for the purpose of descriptive modeling.
F.IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y=f(x).
F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.�B. Focus on linear, quadratic, and exponential functions
F.BF.1 Write a function that describes a relationship between two quantities.�A. Determine an explicit expression, a recursive process, or steps for calculation from context. �I. Focus on linear and exponential functions�II. Focus on situations that exhibit quadratic or exponential relationships.
F.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
3 Function Families of Algebra 1
Greatest Slope (type in below) |
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Least Slope (type in below) |
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Recall: 3 forms of linear equations
Warm-up #1
Using the digits 1 to 9 at most one time each, fill in the boxes to find the greatest and least possible slope
Warm-up #2
Using the digits 1 to 9 at most one time each, fill in the boxes to complete the statement below.
Exploration #1
Write each linear equation in slope-intercept form. Then use a graphing calculator to graph the three equations in the same square viewing window. Which two lines appear parallel? How can you tell?
Exploration #2
Write each linear equation in slope-intercept form. Then use a graphing calculator to graph the three equations in the same square viewing window. Which two lines appear perpendicular? How can you tell?