Unit 4
Modeling Linear RElationships & Functions
IN THIS UNIT STUDENTS WILL BE EXPECTED TO:
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LEARNING OBJECTIVES |
7.PAR.4.7 Use similar triangles to explain why the slope, m, is the same between any two distinct points on a nonvertical line in the coordinate plane.
7.PAR.4.8 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
7.PAR.4.8 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
8.PAR.4.1 Use the equation y = mx (proportional) for a line through the origin to derive the equation y = mx + b (non-proportional) for
a line intersecting the vertical axis at b.
8.PAR.4.2 Show and explain that the graph of an equation representing an applicable situation in two variables is the set of all its solutions plotted in the coordinate plane.
8.FGR.5.1 Show and explain that a function is a rule that assigns to each input exactly one output.
8.FGR.5.2 Within realistic situations, identify and describe examples of functions that are linear or nonlinear. Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
8.FGR.5.3 Relate the domain of a linear function to its graph and where applicable to the quantitative relationship it describes.
8.FGR.5.4 Compare properties (rate of change and initial value) of two functions used to model an authentic situation each
represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
8.FGR.5.5 Write and explain the equations y = mx + b (slope-intercept form), Ax + By = C (standard form), and (y - y1) = m(x - x1)
(point-slope form) as defining a linear function whose graph is a straight line to reveal and explain different properties of the function.
8.FGR.5.6 Write a linear function defined by an expression in different but equivalent forms to reveal and explain different properties
of the function.
8.FGR.5.7 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph.
8.FGR.5.8 Explain the meaning of the rate of change and initial value of a linear function in terms of the situation it models and in terms of its graph or a table of values.
8.FGR.5.9 Graph and analyze linear functions expressed in various algebraic forms and show key characteristics of the graph to describe applicable situations.
7.PAR.4.8 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
7.PAR.4.8 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
8.PAR.4.1 Use the equation y = mx (proportional) for a line through the origin to derive the equation y = mx + b (non-proportional) for
a line intersecting the vertical axis at b.
8.PAR.4.2 Show and explain that the graph of an equation representing an applicable situation in two variables is the set of all its solutions plotted in the coordinate plane.
8.FGR.5.1 Show and explain that a function is a rule that assigns to each input exactly one output.
8.FGR.5.2 Within realistic situations, identify and describe examples of functions that are linear or nonlinear. Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
8.FGR.5.3 Relate the domain of a linear function to its graph and where applicable to the quantitative relationship it describes.
8.FGR.5.4 Compare properties (rate of change and initial value) of two functions used to model an authentic situation each
represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
8.FGR.5.5 Write and explain the equations y = mx + b (slope-intercept form), Ax + By = C (standard form), and (y - y1) = m(x - x1)
(point-slope form) as defining a linear function whose graph is a straight line to reveal and explain different properties of the function.
8.FGR.5.6 Write a linear function defined by an expression in different but equivalent forms to reveal and explain different properties
of the function.
8.FGR.5.7 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph.
8.FGR.5.8 Explain the meaning of the rate of change and initial value of a linear function in terms of the situation it models and in terms of its graph or a table of values.
8.FGR.5.9 Graph and analyze linear functions expressed in various algebraic forms and show key characteristics of the graph to describe applicable situations.
LEARNING TARGET
- I can explain why the slope, m, is the same between any two distinct points.
- I can demonstrate a conceptual understanding of slope.
- I can compare two different proportional relationships given different representations.
- I can identify the similarity of a graph of y = mx and y = mx + b
- I can determine the change of a linear equation when the starting point is not zero.
- I can explain that the graph of an equation represents the set of all its solutions.
- I can analyze a graph to determine if it is a function.
- I can interpret graphs as linear or non-linear.
- I can sketch a graph of a real-world situation to depict the behavior of the function.
- I can determine the domain of a graph and explain its meaning.
- I can compare the properties of two functions presented in different ways using real world situations.
- I can convert an equation in standard form or point-slope form into slope intercept form.
- I can determine the y intercept and slope in a linear equation.
- I can describe the significance of the y intercept and the slope in real world situations.
- I can write a linear function in different forms from a real-world situation.
- I can find the slope and y-intercept given a table, verbal description, and graph
- I can write a linear equation given a table, verbal description, and graph.
- I can use the calculated slope and y-intercept to predict and interpret how they relate to situational data in real world applications.
- Given point-slope formula, standard form, and slope-intercept form of linear equations, I can identify how slope and y-intercept relate to real world situations.