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## Linear Programming

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Write an inequality to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret data points as possible (i.e. a solution) or not possible (i.e. a non- solution) under the established constraints.

## Graphing Linear Equations on a Graphing Calculator

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Graphing Calculator Lesson (TI-84)

Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x² + y² = 3.

## Solving Systems of Linear Equations using Matrices

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Graphing Calculator Lesson (TI-84)

Represent a system of linear equations as a single matrix equation in a vector variable.  Add, subtract, and multiply matrices of appropriate dimensions.

## Graphing Linear Functions

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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.

## Comparing Linear and Exponential Functions

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Distinguish between situations that can be modeled with linear functions and with exponential functions.  Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

## Linear Regression

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Interpret the parameters in a linear or exponential function in terms of a context.  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, quadratic, and exponential models.

## Continuous Linear Function

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Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

## Discrete Linear Functions

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Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.  Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

## Solving Systems of Quadratic and Linear Equations

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Solve quadratic equations in one variable.  Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

## Writing Linear Functions

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Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.  Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.