Math Clip Art--Applications of Linear Functions: Distance vs. Time 06

Topic

Linear Functions

Description

This math clip art image is part of a series illustrating applications of linear functions, specifically modeling the relationship between distance and time. The image introduces the equation f(x) = 30x, which represents the function that models the car's movement. This equation encapsulates the linear relationship between time (x) and distance (f(x)) that has been explored in previous images.

By presenting the algebraic representation alongside the graphical one, this image helps students connect different forms of expressing linear functions. It demonstrates how the constant speed of 30 feet per second translates into the coefficient of x in the equation. This visual aid is crucial in helping students understand the relationship between the graph's slope, the rate of change in the data table, and the coefficient in the linear equation.

Teacher's Script: "Now we're getting to the heart of our linear function. This equation, f(x) = 30x, is like a shorthand way of describing everything we've seen so far. The '30' tells us the car's speed – 30 feet every second. The 'x' represents time. So, for any time 'x', we can quickly calculate the distance 'f(x)'. Let's try it out – if x is 5 seconds, what distance has the car traveled? How about 10 seconds? See how powerful this simple equation is? It captures the essence of the car's entire journey in just a few symbols!"

For a complete collection of math clip art related to Applications of Linear Functions click on this link: Applications of Linear Functions: Distance vs. Time Collection.