Graph Relations

Anika is studying graphs in her math class. She wants to know what makes a graph proportional. Can you help her?

• If the graph is linear

• If the line on the graph goes through the origin

• If the graph has a curvy line

• If the graph is linear and the line goes through the origin

Ethan is analyzing a graph of a car's speed over time. If the graph shows a constant speed, what is the unit rate for this graph?

• 100

• 25

• 50

• 200

Lily, Arjun, and Luna are in a competition. They noticed that Taylor can write at a certain speed. Which statement matches Taylor's writing speed based on the graph?

• Taylor can write 6 words per minute

• Taylor can write 25 words per minute

• Taylor can write 50 words per minute

• Taylor can write 150 words per minute

Benjamin and Daniel are comparing their running speeds. If Benjamin runs at a constant speed and Daniel changes his speed, who has a proportional relationship between distance and time?

• Benjamin

• Daniel

• Neither

Abigail and David are studying a graph of Mason's monthly income and expenses. Does this graph represent a proportional relationship?

• No, because it doesn't pass through the origin.

• Yes, because it doesn't pass through the origin.

• Yes, because it intersects the y axis.

• No, because it intersects the x axis.

Arjun, Jackson, and Elijah are studying the relationship between the number of hours they work at their part-time job and the money they earn. They notice that the graph of this relationship always goes through what point?

• (0,0)

• (10,0)

• (0, 10)

• none of these

Lily, Elijah, and Benjamin are planning a road trip. If their car travels at a constant speed, what would be the unit rate/constant of proportionality of their car's speed?

• 80 miles in 1 hour

• 20 miles in 1 hour

• 40 miles in 1 hour

• 160 miles in 1 hour

Sophia, Evelyn, and Maya took a taxi ride in New York City. They noticed a pattern between the distance the taxi traveled and the cost of their ride. Is this relationship proportional? Explain.

• The relationship is not proportional because the cost does not start at zero when the distance is zero.

• The relationship is proportional because the cost of the ride increases in a straight line as the distance increases.

• The relationship is not proportional because the cost of the ride does not increase in a straight line as the distance increases.

• The relationship is proportional because the cost increases as the distance increases.

Luis can run 2 miles per hour. Which graph

best represents this relationship?

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If f(x) = x² - 2x - 7, graph the parabola.

(graph the vertex first, then one other point)