# MA.8.AR.3.2

Given a table, graph or written description of a linear relationship, determine the slope.

### Clarifications

Clarification 1: Problem types include cases where two points are given to determine the slope.

Clarification 2: Instruction includes making connections of slope to the constant of proportionality and to similar triangles represented on the coordinate plane.

General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Algebraic Reasoning
Date Adopted or Revised: 08/20
Status: State Board Approved

## Related Courses

This benchmark is part of these courses.
1205050: M/J Accelerated Mathematics Grade 7 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1205070: M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812030: Access M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.8.AR.3.AP.2: Given a table or graph of a linear relationship, identify the slope.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Formative Assessments

Deriving Lines - 2:

Students are asked to derive the general equation of a line with a y-intercept of (0, b).

Type: Formative Assessment

Slope Triangles:

Students are asked to use similar triangles to explain why the slope is the same regardless of the points used to calculate it.

Type: Formative Assessment

Deriving Lines - 1:

Students are asked to derive the general equation of a line containing the origin.

Type: Formative Assessment

Profitable Functions:

Students are asked to write a function to model a linear relationship given its graph.

Type: Formative Assessment

Smart TV:

Students are asked to determine the rate of change and initial value of a linear function given a table of values, and interpret the rate of change and initial value in terms of the situation it models.

Type: Formative Assessment

Construction Function:

Students are asked to construct a function to model a linear relationship between two quantities given two ordered pairs in context.

Type: Formative Assessment

Drain the Pool:

Students are asked to determine the rate of change and initial value of a linear function when given a graph, and to interpret the rate of change and initial value in terms of the situation it models.

Type: Formative Assessment

Compare Slopes:

Students are asked to identify, describe and compare the slopes of two proportional relationships given the graph of one and the equation of the other.

Type: Formative Assessment

Proportional Paint:

Students are given a graph of a proportional relationship and asked to determine the unit rate of the relationship and compare it to the slope of the graph.

Type: Formative Assessment

Interpreting Slope:

Students are asked to graph a proportional relationship, given a table of values, and find and interpret the slope.

Type: Formative Assessment

Students are asked to determine the rate of change of two functions presented in different forms (table and graph) and determine which is the greater rate of change within a real-world context.

Type: Formative Assessment

## Lesson Plans

Beginning Linear Functions:

This is a simple lesson used to describe the concept of slope to algebra students. Students will be able to:

• determine positive, negative, zero, and undefined slopes by looking at graphed functions.
• determine x- and y- intercepts by substitution or by examining graphs.
• write equations in slope-intercept form and make graphs based on slope/y-intercept of linear functions.

Type: Lesson Plan

Designing a Skateboard Kicker Ramp:

In this lesson students will design a "Skateboard Kicker Ramp" to discover that slope of similar triangles is the same at any two distinct points.  Students will model with mathematics the concept of slope by looking at the pattern set by similar triangles.

Type: Lesson Plan

Scatter plots, spaghetti, and predicting the future:

Students will construct a scatter plot from given data. They will identify the correlation, sketch an approximate line of fit, and determine an equation for the line of fit. They will explain the meaning of the slope and y-intercept in the context of the data and use the line of fit to interpolate and extrapolate values.

Type: Lesson Plan

## Original Student Tutorials

Hailey’s Treehouse: Similar Triangles & Slope:

Learn how similar right triangles can show how the slope is the same between any two distinct points on a non-vertical line as you help Hailey build stairs to her tree house in this interactive tutorial.

Type: Original Student Tutorial

Constructing Functions From Two Points:

Learn to construct a function to model a linear relationship between two quantities and determine the slope and y-intercept given two points that represent the function with this interactive tutorial.

Type: Original Student Tutorial

Functions, Sweet Functions:

See how sweet it can be to determine the slope of linear functions and compare them in this interactive tutorial. Determine and compare the slopes or the rates of change by using verbal descriptions, tables of values, equations and graphical forms.

Type: Original Student Tutorial

It's a Slippery Slope!:

Learn what slope is in mathematics and how to calculate it on a graph and with the slope formula in this interactive tutorial.

Type: Original Student Tutorial

Scatterplots Part 4: Equation of the Trend Line:

Learn how to write the equation of a linear trend line when fitted to bivariate data in a scatterplot in this interactive tutorial.

This is part 4 in 6-part series. Click below to open the other tutorials in the series.

Type: Original Student Tutorial

## Perspectives Video: Professional/Enthusiast

Slope and Deep Sea Sharks:

Shark researcher, Chip Cotton, discusses the use of regression lines, slope, and determining the strength of the models he uses in his research.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

## Teaching Idea

Now That is a Dense Graph:

In this activity, the density of ethanol is found by graphical means. In the second part, the density of sodium thiosulfate is found, also by graphical means. The values found are then analyzed statistically.

Type: Teaching Idea

## Video/Audio/Animation

Slope:

"Slope" is a fundamental concept in mathematics. Slope of a linear function is often defined as " the rise over the run"....but why?

Type: Video/Audio/Animation

## MFAS Formative Assessments

Compare Slopes:

Students are asked to identify, describe and compare the slopes of two proportional relationships given the graph of one and the equation of the other.

Construction Function:

Students are asked to construct a function to model a linear relationship between two quantities given two ordered pairs in context.

Deriving Lines - 1:

Students are asked to derive the general equation of a line containing the origin.

Deriving Lines - 2:

Students are asked to derive the general equation of a line with a y-intercept of (0, b).

Drain the Pool:

Students are asked to determine the rate of change and initial value of a linear function when given a graph, and to interpret the rate of change and initial value in terms of the situation it models.

Interpreting Slope:

Students are asked to graph a proportional relationship, given a table of values, and find and interpret the slope.

Profitable Functions:

Students are asked to write a function to model a linear relationship given its graph.

Proportional Paint:

Students are given a graph of a proportional relationship and asked to determine the unit rate of the relationship and compare it to the slope of the graph.

Slope Triangles:

Students are asked to use similar triangles to explain why the slope is the same regardless of the points used to calculate it.

Smart TV:

Students are asked to determine the rate of change and initial value of a linear function given a table of values, and interpret the rate of change and initial value in terms of the situation it models.

Students are asked to determine the rate of change of two functions presented in different forms (table and graph) and determine which is the greater rate of change within a real-world context.

## Original Student Tutorials Mathematics - Grades 6-8

Constructing Functions From Two Points:

Learn to construct a function to model a linear relationship between two quantities and determine the slope and y-intercept given two points that represent the function with this interactive tutorial.

Functions, Sweet Functions:

See how sweet it can be to determine the slope of linear functions and compare them in this interactive tutorial. Determine and compare the slopes or the rates of change by using verbal descriptions, tables of values, equations and graphical forms.

Hailey’s Treehouse: Similar Triangles & Slope:

Learn how similar right triangles can show how the slope is the same between any two distinct points on a non-vertical line as you help Hailey build stairs to her tree house in this interactive tutorial.

Scatterplots Part 4: Equation of the Trend Line:

Learn how to write the equation of a linear trend line when fitted to bivariate data in a scatterplot in this interactive tutorial.

This is part 4 in 6-part series. Click below to open the other tutorials in the series.

## Original Student Tutorials Mathematics - Grades 9-12

It's a Slippery Slope!:

Learn what slope is in mathematics and how to calculate it on a graph and with the slope formula in this interactive tutorial.

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Original Student Tutorials

Hailey’s Treehouse: Similar Triangles & Slope:

Learn how similar right triangles can show how the slope is the same between any two distinct points on a non-vertical line as you help Hailey build stairs to her tree house in this interactive tutorial.

Type: Original Student Tutorial

Constructing Functions From Two Points:

Learn to construct a function to model a linear relationship between two quantities and determine the slope and y-intercept given two points that represent the function with this interactive tutorial.

Type: Original Student Tutorial

Functions, Sweet Functions:

See how sweet it can be to determine the slope of linear functions and compare them in this interactive tutorial. Determine and compare the slopes or the rates of change by using verbal descriptions, tables of values, equations and graphical forms.

Type: Original Student Tutorial

It's a Slippery Slope!:

Learn what slope is in mathematics and how to calculate it on a graph and with the slope formula in this interactive tutorial.

Type: Original Student Tutorial

Scatterplots Part 4: Equation of the Trend Line:

Learn how to write the equation of a linear trend line when fitted to bivariate data in a scatterplot in this interactive tutorial.

This is part 4 in 6-part series. Click below to open the other tutorials in the series.

Type: Original Student Tutorial

## Video/Audio/Animation

Slope:

"Slope" is a fundamental concept in mathematics. Slope of a linear function is often defined as " the rise over the run"....but why?

Type: Video/Audio/Animation

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.