Exploring Proportional Graphs and Relationships

This lesson introduces graphs of proportional relationships, emphasizing that they form a straight line through the origin (0,0). It explains how to identify proportional graphs by checking these characteristics and demonstrates finding the constant of proportionality by dividing y-values by x-values. The lesson also covers identifying non-proportional graphs, which either do not form a straight line or do not pass through the origin. The session concludes with a recap of the key points: proportional graphs are straight lines that pass through the origin.

What is a key feature of the graph of a proportional relationship?

• It has a constant y-intercept.

• It forms a curve.

• It passes through the point (1,1).

• It forms a straight line through the origin.

What is the origin in a coordinate plane?

• The point (0,0)

• The point (1,0)

• The point (1,1)

• The point (0,1)

How can you determine the constant of proportionality from a graph?

• By dividing the x-values by the y-values.

• By finding the y-value when x is 1.

• By finding the x-value when y is 1.

• By adding the x and y values.

If the y-value is 12 when the x-value is 2, what is the constant of proportionality?

• 8

• 6

• 4

• 10

Why is a graph not considered proportional if it does not form a straight line?

• Because it does not have an x-intercept.

• Because it does not have a constant slope.

• Because it does not have a y-intercept.

• Because it does not pass through the origin.

Why is a graph not proportional if it does not pass through the origin?

• Because it does not have a constant slope.

• Because it does not start at (0,0).

• Because it does not form a straight line.

• Because it does not have a y-intercept.

What are the two main characteristics of a proportional relationship graph?

• It forms a curve and has a constant slope.

• It forms a straight line and has a constant y-intercept.

• It forms a straight line and passes through the origin.

• It forms a curve and passes through (1,1).

What is the main takeaway about the graphs of proportional relationships?

• They always form a straight line through the origin.

• They always pass through (1,1).

• They always form a curve.

• They always have a constant y-intercept.