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Exploring Linear Functions and Slope: Equations and Predictive Analysis

This lesson focuses on using slope to write equations for linear functions. We will examine points on a line, identify which points are not aligned, and explore relationships between chirps of crickets and temperature. Through practice problems, such as calculating call costs based on duration, we will learn to derive equations representing these relationships. Key concepts include determining coordinates of points on a line, identifying non-collinear points, and predicting outputs from linear relationships using slope-intercept form.

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Exploring Linear Functions and Slope: Equations and Predictive Analysis

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  1. Using Slope to Write Equations for Linear Functions

  2. Warm Up • 1. The points whose coordinates are (3,1), (5,-1), and (7,-3) all lie on the same line. What could be the coordinates of another point on that line? Explain. • 2. Of the points (0,5), (2,4), (3,3) and (6,2), which one does not lie on the same line as the other three? Explain.

  3. Crickets

  4. Cricket Chirpshttp://tinyurl.com/cricketsmath • Biologists have found that the number of chirps some crickets make per minute is related to the temperature. The relationship is very close to being linear. When crickets chirp 124 times a minute, it is about 68 degrees Fahrenheit. When they chirp 172 times a minute, it is about 80 degrees Fahrenheit. How can we predict the number of chirps for any temperature?

  5. Practice • Suppose a 5-minute overseas call costs $5.91 and a 10-minute call costs $10.86. The cost of the call and the length of the call are related. How could we find the cost of a call of any length?

  6. Exit - Closure • Two points lie on the same straight line. The points are (-2,3) and (6,y). Can we find the value of y? Explain. • Write the equation of a line that passes through the following points: • (4,5) and (-3,5) • (-1,8) and (-1,2)

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