Fellow: Brooke Odle Teacher: Maria Sanchez School: St. Vincent Academy Date: January 9, 2012 Equations of Lines.

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Presentation transcript:

Fellow: Brooke Odle Teacher: Maria Sanchez School: St. Vincent Academy Date: January 9, 2012 Equations of Lines

Objectives Write and graph equations of lines Vernier activity: Record distance versus time data for a person walking at a constant rate. Analyze the data to extract slope and intercept information. Interpret the slope and intercept information for physical meaning.

Equations of Lines: A review Linear Equation: An equation whose graph is a straight line Y-intercept: The y-value of the point where a line crosses the y-axis Slope-intercept form: The form of a linear equation written as y = mx + b, Where m = slope and b = y-intercept

Vernier Activity: Walk the Line When one quantity changes at a constant rate with respect to another, they are linearly related. In math, we describe this relationship by defining a linear equation. In real-world applications, some quantities are linearly- related and can be represented by using a straight-line graph. Ex: Distance versus time

Vernier Activity: Walk the Line Objectives: Record distance versus time data for a person walking at a constant rate. Analyze the data to extract slope and intercept information. Interpret the slope and intercept information for physical meaning. Materials: Laptop Vernier Logger Pro software Vernier Lab Pro Motion Detector Volunteer

Data Table Y-intercept b Optimized slope m Optimized line equation x1,y1x1,y1 x 2,y 2 Slope Regression line equation How does this value compare with the slope you found by trial and error?

Follow-up Questions 1. How do the values of the slope and intercept as determined by Logger Pro compare to your earlier values? Would you expect them to be different? 2. Slope is defined as change in y-values divided by change in x-values. In this activity, slope represents a change in ________ divided by a change in ________. 3. What are the units of measurement for slope in this activity?

Challenge Question The y-intercept can be interpreted as the starting position or the starting distance from the Motion Detector. What does the slope represent physically? Hint: Consider the units of measurement for the slope you described in the previous question.