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How do we derive the equation of a line?

How do we derive the slope-intercept form of a
line?

What is the equation of the trend line of the
scatter plot?

How are the properties of functions
comparable in multiple representations?

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Students identify the rate of change (slope) and initial value (y-intercept) from tables, graphs, equations or verbal descriptions. (Include cases where the axis interval is not one)

Students will interpret 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.

Students will write the equation for a horizontal and a vertical line, identifying the slope as zero or undefined.

Students will write the equation of a line given different criteria (two points, the slope and one
point).

Students will write the equation of a line given different representations (a table, a graph, a verbal situation).

Students will construct a function to model a linear relationship between two quantities.

Students will be able to understand how to compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

Students derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

Students will use similar triangles to see the fact that the slope is constant between any two distinct points on a non-vertical line in the plane.

Students will understand that a line will model relationships between two quantitative variables.

Students will understand interpreting the slope and intercept of the line of best fit in the context of
the data.

Students will understand how to read a scatter plot.

Students will be able to give the form, correlation and direction of a scatterplot.

Students will understand that the form includes linear and non-linear.

Students will understand that the correlation includes strong, moderate, and weak.

Students will understand that the direction of a scatterplot can be positive, negative, constant and no correlation.

Students will understand what the meaning of an outlier is and what it represents.

Students will be able to graph the best fit line.

Students will be able to write the equation of the line of best fit.

Students will understand how to create and interpret scatter plots, focusing on outliers, positive or negative association, linearity or curvature.

Students will extend their descriptions and understanding of variation to the graphical displays of
bivariate data.

Students will understand how to draw a line of best fit for a scatter plot and informally measure the strength of fit.

Students will be able to make predictions based on the line of best fit.

Students will understand how create a two way table.

Students will be able to construct and interpret scatter plots for bivariate measurement data to
investigate patterns of association between two quantities.

Students will understand how to describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

Students will understand how to use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

Students will understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table.

Students will understand how to construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects.

Students will understand how to use relative frequencies calculated for rows or columns to describe
possible association between the two variables.

Students will be able to determine which function has the highest rate of change or initial value when the functions are in the same form.

Students will be able to determine which function has the highest rate of change or initial value when the functions are in different forms.

Students will be able to interpret the rate of change and the initial value in context.

Students will be able to determine where a function is increasing or decreasing.

Students will be able to interpret distance-time graphs.

Students will graph proportional relationships, interpreting the unit rate as the slope of the graph.

Students will describe qualitatively the functional relationship between two quantities by analyzing
a graph.

Students will compare properties of two functions each represented in a different way
(algebraically, graphically, numerically in tables, or by verbal descriptions).

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PRIORITY:
F.2​ Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

EE.6​ Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical
line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for
a line intercepting the vertical axis at b.

SP.2​ Know that straight lines are widely used to model relationships between two quantitative variables. For scatter
plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the
closeness of the data points to the line.

SUPPORTING:
F.4​ 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. Interpret 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.

F.5​ Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the
function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a
function that has been described verbally.

EE.5​ Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different
proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

SP.1​ Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association
between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear
association, and nonlinear association.

SP.3​ Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5
cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature
plant height.

SP.4 ​ Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two
categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.

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Analyze
Construct
Model
Interpret
Construct
Develop
Determine
State
Categorize
Characteristics
Attributes
Compare
Qualitative

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Linear function
Non-linear function
Input
Output
Unit rate
Rate of change
Initial value
Slope
Similar triangles
Non-vertical line
Trend line
Line of Best fit
Bivariate Data
Correlation
Causation
Positive Correlation
Negative Correlation
No Correlation
Scatter plots
Outliers
Categorical Variable
Two-way table
Frequency
Marginal Frequency
Joint frequency

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Scatter plots: studying, shoe size, and test scores

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Sal answers a question about scatter plots that show the relationship between study time, shoe size, and test score.

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Constructing a scatter plot

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Practice plotting points to construct a scatter plot.

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Describing trends in scatter plots

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Practice making sense of trends in scatter plots. That is, explain what trends mean in terms of real-world quantities.

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Unit 4- Scatter plots and Two-way tables Review

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Introduction to Scatter Plots (12 Scenarios each for positive, negative, and no correlation)

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The slope of a line is rise over run. Learn how to calculate the slope of the line in a graph by finding the change in y and the change in x.

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Estimating the line of best fit exercise

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Sal solves a problem where he has to estimate the line of best fit for a scatter plot.

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Sal interprets a trend line that shows the relationship between study time and math test score for Shira.

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Eyeballing the line of best fit

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Given a random assortment of points, draw a line of best fit through them.

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using the graphing calculator in secondary mathematics

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Estimating equations of lines of best fit, and using them to make predictions

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Estimating equations of lines of best fit, and using them to make predictions

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Practice estimating the equation of a line of best fit through data points in a scatter plot. Then, use the equation to make a prediction.

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Estimating the line of best fit exercise

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Sal solves a problem where he has to estimate the line of best fit for a scatter plot.