Exploring the Constant of Proportionality in Graphs

This video tutorial explains how to represent direct proportions graphically. It covers the characteristics of direct proportion graphs, such as being a straight line passing through the origin. The tutorial provides examples of graphs that are and aren't direct proportions and demonstrates how to find the constant of proportionality. It also explains how to write direct proportion equations using the constant of proportionality. Additional examples are provided to reinforce the concepts.

What is a characteristic feature of a direct proportion graph?

• It is a curved line.

• It never intersects the x-axis.

• It passes through the origin (0,0).

• It only increases in value.

How can you identify a graph as directly proportional?

• The line goes through the point (1,1).

• The graph represents exponential growth.

• The line is horizontal.

• The graph is a straight line through the origin.

What is the first step in finding the constant of proportionality from a graph?

• Calculate the slope of the graph.

• Select any point on the graph.

• Draw a tangent line at the origin.

• Identify a point where the graph intersects grid lines.

What does the constant of proportionality represent in a direct proportion?

• The slope of the graph.

• The difference between consecutive y-values.

• The x-intercept of the graph.

• The maximum value of y.

How do you calculate the constant of proportionality from a graph?

• Add the x and y values of a point.

• Find the average of the x and y values of all points.

• Divide the y-value by the x-value of a chosen point.

• Multiply the x and y values of a point.

What equation form is used to represent a direct proportion?

• y = k/x

• y = kx

• y = k + x

• y = x/k

In the context of direct proportions, what does 'k' stand for?

• The variable on the x-axis.

• The variable on the y-axis.

• The constant of proportionality.

• The slope of the y-axis.

What is the significance of a graph passing through the origin in the context of direct proportions?

• It signifies that the variables are inversely proportional.

• It shows the graph is non-linear.

• It indicates exponential growth.

• It confirms the relationship is directly proportional.

How can you verify if a graph represents a direct proportion?

• Making sure it's a vertical line.

• Confirming it's a straight line that passes through the origin.

• Ensuring it's a curved line.

• By checking if it's a straight line that doesn't pass through the origin.

What is the correct way to write a direct proportion equation?

• x = ky

• y/x = k

• y = k + x

• y = kx