Moving Straight Ahead: Linear Relationships
Linear Relationships: Recognize problem situations in which two or more variables have a linear relationship to each other.
- Identify and describe the patterns of change between the independent and dependent variables for linear relationships represented by tables, graphs, equations, or contextual settings
- Construct tables, graphs, and symbolic equations that represent linear relationships
- Identify the rate of change between two variables and the x- and y-intercepts from graphs, tables, and equations that represent linear relationships
- Translate information about linear relationships given in a context, a table, a graph, or an equation to one of the other forms
- Write equations that represent linear relationships given specific pieces of information, and describe what information the variables and numbers represent
- Make a connection between slope as a ratio of vertical distance to horizontal distance between two points on a line and the rate of change between two variables that have a linear relationship
- Recognize that y = mx represents a proportional relationship
- Solve problems and make decisions about linear relationships using information given in tables, graphs, and equations
Equivalence: Understand that the equality sign indicates that two expressions are equivalent.
- Recognize that the equation y = mx + b represents a linear relationship and means that mx + b is an expression equivalent to y
- Recognize that linear equations in one unknown, k = mx + b or y = m(t) + b, where k, t, m, and b are constant numbers, are special cases of the equation y = mx + b
- Recognize that finding the missing value of one of the variables in a linear relationship,y = mx + b, is the same as finding a missing coordinate of a point (x, y) that lies on the graph of the relationship
- Solve linear equations in one variable using symbolic methods, tables, and graphs
- Recognize that a linear inequality in one unknown is associated with a linear equation
- Solve linear inequalities using graphs or algebraic reasoning
- Solve linear inequalities using graphs or algebraic reasoning
- Write and interpret equivalent expressions
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