**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**8

**Strand:**Algebraic Reasoning

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## Benchmark Instructional Guide

### Connecting Benchmarks/Horizontal Alignment

### Terms from the K-12 Glossary

- Intercept
- Slope

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

In grade 7, students translated between different representations of proportional relationships. In grade 8, students write an equation in slope-intercept form from a written description, a table, or a graph. In Algebra 1, students write a linear two-variable equation to represent a relationship given by a variety of mathematical and real-world contexts.- Point-slope form and standard forms are not expectations at this grade level.
- Instruction connects proportional relationships to support the generation of the equation $y$ = $m$$x$ + $b$. Helping students see how the linear equation is both the same and different from the proportional relationship will support the appropriate use of proportional thinking using the rate of change.
- Using an online dynamic graphing tool to explore how the graph changes as either the slope or the $y$-intercept changes helps students visualize the coefficients and constants in the equation
*(MTR.4.1).* - Students should recognize in a table that the $y$-intercept is the $y$-value when $x$ is equal to 0. The slope can be determined by finding the ratio between the change in two $y$-values and the change between the two corresponding $x$-values.
- Using graphs, students identify the $y$-intercept as the point where the line crosses the $y$-axis and the slope as the vertical change divided by the horizontal change. In a linear equation, the coefficient of $x$ is the slope and the constant is the $y$-intercept. Students need to be given the equations in formats other than $y$ = $m$$x$ + $b$, such as $y$ = $a$$x$ + $b$ or $y$ = $b$ + $m$$x$.
- Instruction includes using a variety of vocabulary to make connections to real-world
- concepts and future courses. To describe the slope, one can say either “the vertical change divided by the horizontal change” or “rise over run.”
- The instruction includes examples where the slope is positive or negative and the ??intercept is given as a positive or a negative in the equation.
- When providing a graph, be sure there are easily identifiable points for students to use in calculating the slope.
- Instruction allows students to make connections between the different representations of a linear relationship
*(MTR.2.1).*

### Common Misconceptions or Errors

- Students may incorrectly identify the values for the slope and $y$-intercept.
- Students may incorrectly calculate the slope with a common error of inverting the change in $y$ and the change in $x$.

### Strategies to Support Tiered Instruction

- Teacher supports students who incorrectly identify the values for the slope and $y$-intercept by providing opportunities to notice patterns between a given value for $b$, a line graphed on the coordinate plane, and a given equation of the same line.
- Teacher supports students who incorrectly calculate the slope by inverting the change in $y$ and the change in $x$ using error analysis tasks, in which the expression is incorrectly written as , and has students find and correct the error.
- Teacher supports students who invert the $x$ and $y$ values when calculating slope by using real-world problems that students can relate to and helping students represent the relationship visually.
- Teacher co-creates an anchor chart naming the slope and $y$-intercept of a given line and then discusses where to start when graphing the line.
- Instruction incudes graphing various linear equations from a table and then discussing the pattern students notice in regard to the $y$-intercept.
- Teacher provides students with graphs and equations of several linear equations then co-illustrates connections between the slopes and $y$-intercepts of each line to the corresponding parts of each equation using the same color highlights.
- Teacher co-creates a graphic organizer with students to include examples of positive and negative slope; the meaning of each variable in slope intercept form; and how to determine the slope and $y$-intercept in a table, graph and verbal description.

### Instructional Tasks

*Instructional Task 1*

**(MTR.7.1)**Victoria owns a store that sells board games. She made the following graph to relate the number of board games she sells to her overall profits.

- Part A. Write an equation in slope-intercept form to describe this relation. Explain how to determine the equation.
- Part B. What is the meaning of the $y$-intercept in the given context? What is the meaning of the slope in the given context?

### Instructional Items

*Instructional Item 1*

Write an equation that represents the graph shown.

*Instructional Item 2*

The table shown represents a linear relationship. Using the table, write an equation in slope-intercept form.

**The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.*

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Original Student Tutorials

## Perspectives Video: Professional/Enthusiast

## Teaching Idea

## MFAS Formative Assessments

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

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

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

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

Students are asked to construct a function to model a linear relationship between two quantities given a table of values.

## Original Student Tutorials Mathematics - Grades 6-8

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.

Learn to construct linear functions from tables that contain sets of data that relate to each other in special ways as you complete this interactive tutorial.

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.

## Student Resources

## Original Student Tutorials

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

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.

- Scatterplots Part 1: Graphing
- Scatterplots Part 2: Patterns, Associations and Correlations
- Scatterplots Part 3: Trend Lines
- Scatterplots Part 5: Interpreting the Equation of the Trend Line
- Scatterplots Part 6: Using Linear Models

Type: Original Student Tutorial

Learn to construct linear functions from tables that contain sets of data that relate to each other in special ways as you complete this interactive tutorial.

Type: Original Student Tutorial