Let’s use lines to think about situations.
Illustrative Math Unit 8.4, Lesson 11 (printable worksheets)
The following diagram show how to use graphs to find an ordered pair that two real-world situations have in common.
Now suppose another car, Car C, had also passed the rest stop at time t = 0 and traveled in the same direction as Car A, also going 75 miles per hour. It’s equation would also be d = 75t. Any solution to the equation for Car A would also be a solution for Car C, and any solution to the equation for Car C would also be a solution for Car A. The line for Car C would land right on top of the line for Car A. In this case, every point on the graphed line is a solution to both equations, so that there are infinitely many solutions to the question “when are Car A and Car C the same distance from the rest stop?” This would mean that Car A and Car C were side by side for their whole journey.
When we have two linear equations that are equivalent to each other, like y = 3x + 2 and 2y = 6x + 4, we will get two lines that are “right on top” of each other. Any solution to one equation is also solution to the other, so these two lines intersect at infinitely many points.
What do you notice? What do you wonder?
A different ant and ladybug are a certain distance apart, and they start walking toward each other. The graph shows the ladybug’s distance from its starting point over time and the labeled point (2.5,10) indicates when the ant and the ladybug pass each other.
The ant is walking 2 centimeters per second.
Elena and Jada were racing 100 meters on their bikes. Both racers started at the same time and rode at constant speed. Here is a table that gives information about Jada’s bike race:
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