Exploring Graphs of Proportional Relationships

The video tutorial introduces graphs of proportional relationships, focusing on their characteristics and differences from other graphs. It includes activities like plotting points, analyzing t-shirt sales data, and graphing cherries to illustrate proportionality. The lesson emphasizes that proportional graphs form a straight line through the origin and discusses real-world applications. Students engage in matching activities using Desmos and conclude with a cooldown exercise to identify non-proportional graphs.

What is the first step in plotting points for a graph of proportional relationships?

• Start with the highest value

• Identify the origin

• Plot along the x-axis first

• Plot along the y-axis first

What does the x-value represent in the t-shirt sale example?

• The size of t-shirts

• The number of t-shirts

• The price per t-shirt

• The total cost of t-shirts

What does the y-value represent in the t-shirt sale example?

• The color of t-shirts

• The size of t-shirts

• The total cost of t-shirts

• The number of t-shirts

What does the constant of proportionality represent in the t-shirt example?

• The total number of t-shirts available

• The price per t-shirt

• The discount on bulk purchases

• The total cost for all t-shirts

Can you buy half of a t-shirt according to the graph discussed?

• No, because a t-shirt is a whole item

• Yes, at half the price

• Yes, but only in special cases

• No, because it's not allowed in the store

Is it possible to buy zero t-shirts according to the graph?

• Yes, and it costs nothing

• No, you must buy at least one

• Yes, but it costs half the price of one t-shirt

• No, because zero is not represented on the graph

Why can't you buy half of a t-shirt in the given example?

• Because half a t-shirt is not a standard sale item

• Because the store does not sell t-shirts in fractions

• Because the graph does not allow for fractional quantities

• Because it's not physically possible to have half a t-shirt

In the context of cherries, why can points on the graph be connected with a line?

• Because cherries can be bought in any quantity, including fractions

• Because cherries are sold by the shirt

• Because the price of cherries never changes

• Because you can buy a whole number of cherries only

What always holds true for graphs of proportional relationships?

• They must form a curved line

• They represent non-proportional relationships as well

• They start anywhere on the graph

• They always form a straight line starting at the origin

What indicates a proportional relationship in a graph?

• A curved line through the origin

• A straight line not passing through the origin

• Disconnected points

• A straight line passing through the origin