On Both of the Lines

The figure below shows an Ant and Ladybug moving towards eachother. Study their movements and answer the questions below.

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Complete a Table of Values.

A farm has chickens and cows. All the cows have 4 legs and all the chickens have 2 legs. All together, there are 82 cow and chicken legs on the farm.

(1). Complete the table to show some possible combinations of chickens and cows to get 82 total legs.

Here is a graph that shows possible combinations of chickens and cows that add up to 30 animals:

(2). If the farm has 30 chickens and cows, and there are 82 chicken and cow legs all together, then how many chickens and how many cows could the farm have?

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Graph a Relationship from a Table of Values.

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:

(1). Graph the relationship between distance and time for Jada’s bike race. Make sure to label and scale the axes appropriately.

(2). Elena traveled the entire race at a steady 6 meters per second. On the same axes above, graph the relationship between distance and time for Elena’s bike race.

(3). Who won the race?

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Question Set.

For each equation, decide if it is always true or never true.

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Diego has $11 and begins saving $5 each week toward buying a new phone. At the same time that Diego begins saving, Lin has $60 and begins spending $2 per week on supplies for her art class.

(1). Is there a week when they have the same amount of money? 

(2). How much do they have at that time?

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Use the graph to find x and y values that make both equations listed true.

(1). What is the point where both and = 2 – 5 are true?

(2). The point where the graphs of two equations intersect has -coordinate 2. One equation is = -3 + 5. Find the other equation if its graph has a slope of 1.

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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 point (2.5, 10) indicates when the ant and ladybug pass each other.

The ant is walking 2 centimeters per second.

(1). Write an equation representing the relationship between the ant’s distance from the ladybug’s starting point and the amount of time that has passed.

(2). If you haven’t already, draw the graph of your equation on the same coordinate plane.