Graphical Representations of Proportion

The video tutorial covers the concept of proportions, starting with direct proportion where y is proportional to x, forming a linear graph. It explains how the constant of proportionality, k, affects the graph's steepness. The tutorial then moves to non-linear relationships, showing how increasing the power of x results in steeper curves. It also covers inverse proportion, where y equals k over x, and explains the graph's behavior, including asymptotes. Finally, it discusses inverse proportion with x squared, highlighting how squaring negative numbers affects the graph.

What happens to the graph of a direct proportion when the constant of proportionality, k, increases?

• The line becomes steeper.

• The line becomes flatter.

• The line curves upwards.

• The line remains unchanged.

In a non-linear relationship, what happens to the curve when the power of x is increased?

• The curve remains unchanged.

• The curve becomes a straight line.

• The curve becomes steeper.

• The curve becomes flatter.

Which of the following represents an inverse proportion?

• y = k/x

• y = kx^2

• y = kx

• y = kx^3

What is an asymptote in the context of inverse proportion graphs?

• A point where the graph intersects the y-axis.

• A line that the graph crosses multiple times.

• A line that the graph approaches but never touches.

• A point where the graph intersects the x-axis.

Why do y-values become positive when x is squared in an inverse proportion graph?

• Because the constant k is positive.

• Because the graph is symmetrical.

• Because squaring a negative number results in a positive value.

• Because x is always positive.