Graphing linear equations and functions
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Defining a Line with Two Points
Place two points wherever you like. Compute the slope of the line between them. View the equation of that line in slope‑intercept … and point‑slope form.
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Direct Variation
Adjust the constant of variation and explore how the graph of the direct variation function changes in response.
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Distance-Time and Velocity-Time Graphs
Create a graph of a runner's position versus time and watch the runner run a 40-yard dash based on the graph you made. Notice the … connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time.
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Distance-Time and Velocity-Time Graphs
Create a graph of a runner's position versus time and watch the runner run a 40-meter dash based on the graph you made. Notice the … connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time.
- METRIC
- Lesson Info
- Launch Gizmo
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Distance-Time Graphs
Create a graph of a runner's position versus time and watch the runner complete a 40-yard dash based on the graph you made. Notice … the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs.
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Distance-Time Graphs
Create a graph of a runner's position versus time and watch the runner complete a 40-meter dash based on the graph you made. Notice … the connection between the slope of the line and the speed of the runner. What will the runner do if the slope of the line is zero? What if the slope is negative? Add a second runner (a second graph) and connect real-world meaning to the intersection of two graphs.
- METRIC
- Lesson Info
- Launch Gizmo
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Introduction to Functions
Determine if a relation is a function using the mapping diagram, ordered pairs, or the graph of the relation. Drag arrows from the domain … to the range, type in ordered pairs, or drag points to the graph to add inputs and outputs to the relation.
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Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear.
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Lines of Best Fit Using Least Squares - Activity A
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit.
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Lines of Best Fit Using Least Squares - Activity B
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit.
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Point-Slope Form of a Line - Activity A
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response.
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Point-Slope Form of a Line - Activity B
Compare the point‑slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response.
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Points in the Coordinate Plane - Activity A
Identify the coordinates of points in the coordinate plane. Drag the points in the plane and investigate how the coordinates change … in response.
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Points in the Coordinate Plane - Activity B
Identify the coordinates of a point in the coordinate plane. Drag the point in the plane and investigate how the coordinates change … in response.
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Points in the Coordinate Plane - Activity C
Identify the coordinates of a point in the coordinate plane. Drag the point in the plane and investigate how the coordinates change … in response.
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Reflections of a Linear Function
Explore and compare the graphs of y = f(x), y = −f(x), y = f(‑x), and y = −f(‑x), for a … linear function f(x) in slope‑intercept form. Vary the terms of f(x) and examine how the graphs change in response.
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Simple and Compound Interest
Find the current balance and the interest charged on an investment using the graph of the interest function and by directly calculating.
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Slope - Activity A
Adjust the coordinates of two points in the plane and find the slope of the line that passes through them.
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Slope - Activity B
Explore the slope of a line, and learn how to calculate slope. Adjust the line by moving points that are on the line, and see how its … slope changes.
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Slope - Activity C
Examine the graph of two points in the plane. Find the slope of the line that passes through the two points. Drag the points and … investigate the changes to the slope and to the coordinates of the points.
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Slope-Intercept Form of a Line - Activity A
Compare the slope‑intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response.
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Slope-Intercept Form of a Line - Activity B
Compare the slope‑intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response.
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Slope-Intercept Form of a Line - Activity C
Compare the slope‑intercept form of a linear equation to its graph. Find the slope of the line using a right triangle on the … graph. Vary the coefficients and explore how the graph changes in response.
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Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response.
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Translating and Scaling Functions
Vary the coefficients in the equation of a function and examine how the graph of the function is translated or scaled. Select … different functions to translate and scale, and determine what they have in common.
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Using Tables, Rules and Graphs
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the … line. Examine how the rule and table change.
