**Maryland College and Career-Ready Education Standards**. Linear relationships refer to two quantities that are related with a linear equation. Since a linear equation is a line, a linear relationship refers to two quantities on a line and their relationship to one another. This relationship can be direct or inverse. If y varies directly as x, it means if y is doubled, then x is doubled. The formula for a direct variation is y = kx, where k is the constant of variation. Read More...

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Study GuideLinear relationshipsWorksheet/Answer key

Linear relationshipsWorksheet/Answer key

Linear relationshipsWorksheet/Answer key

Linear relationships

MD.MA.8.EE. Expressions and Equations (EE)

Understand the connections between proportional relationships, lines, and linear equations.

8.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.

8.EE.5.3. Ability to understand that all proportional relationships start at the origin.

8.EE.5.4. Ability to recognize and apply direct variation.

MD.MA.8.SP. Statistics and Probability (SP)

Investigate patterns of association in bivariate data.

8.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.

8.SP.2.1. See the skills and knowledge that are stated in the Standard.

MD.MA.AI. Algebra I

Unit 1: Relationships between Quantities and Reasoning with Equations

HSA-SSE.A. Interpret the structure of expressions.

A.SSE.1a. Interpret expressions that represent a quantity in terms of its context – Interpret parts of an expression, such as terms, factors, and coefficients.

A.SSE.1a.1. Ability to make connections between symbolic representations and proper mathematics vocabulary.

A.SSE.1b. Interpret expressions that represent a quantity in terms of its context – Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)^n as the product of P and a factor not depending on P.

A.SSE.1b.1. Ability to interpret and apply rules for order of operations.

Unit 2: Linear and Exponential Relationships

HSA-REI.D. Represent and solve equations and inequalities graphically.

A.REI.12. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

A.REI.12.1. Ability to explain why a particular shaded region represents the solution of a given linear inequality or system of linear inequalities.

A.REI.12.2. Ability to convey the mathematics behind the dotted versus solid boundary lines used when graphing the solutions to linear inequalities.

Unit 3: Descriptive Statistics

HSS-ID.B. Summarize, represent, and interpret data on two categorical and quantitative variables.

S.ID.6a. Represent data on two quantitative variables on a scatter-plot, and describe how the variables are related – Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear and exponential models.

S.ID.6a.1. Ability to recognize types of relationships that lend themselves to linear and exponential models.

S.ID.6a.2. Ability to create and use regression models to represent a contextual situation.

S.ID.6b. Represent data on two quantitative variables on a scatter-plot, and describe how the variables are related – Informally assess the fit of a function by plotting and analyzing residuals.

S.ID.6b.1. Ability to create a graphic display of residuals.

S.ID.6b.2. Ability to recognize patterns in residual plots.

S.ID.6b.3. Ability to calculate error margins (residuals) with a calculator.

S.ID.6b.4. Ability to analyze the meaning of patterns in residual plots.

S.ID.6c. Represent data on two quantitative variables on a scatter-plot, and describe how the variables are related – Fit a linear function for a scatter plot that suggests a linear association.

S.ID.6c.1. Ability to recognize a linear relationship displayed in a scatter plot.

MD.MA.AII. Algebra II

Unit 2: Trigonometric Functions

HSS-ID.B. Summarize, represent, and interpret data on two categorical and quantitative variables.

S.ID.6a. Represent data on two quantitative variables on a scatter-plot, and describe how the variables are related – Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear and exponential models.

S.ID.6a.1. Ability to recognize types of relationships that lend themselves to linear and exponential models.

S.ID.6a.2. Ability to create and use regression models to represent a contextual situation.

Standards