Proportional and Non-Proportional Relationships

The video tutorial explains linear and non-proportional relationships, focusing on graphing equations like y = 2x and y = x + 2. It covers the concept of constant slope and the importance of passing through the origin for proportional relationships. The tutorial also includes a non-linear example to illustrate the absence of a constant slope.

What is a key requirement for a relationship to be considered proportional?

• The line must be curved.

• The line must pass through the origin.

• The slope must be variable.

• The line must be horizontal.

When graphing y = 2x, what is the result when x = -1?

• y = 0

• y = 2

• y = -2

• y = -1

How can you determine if a line has a constant slope?

• By ensuring the line is horizontal.

• By checking if the line is curved.

• By checking if the line is vertical.

• By using the rise over run method.

What is the y-intercept of the equation y = x + 2?

• 0

• 1

• 2

• 3

Why is the equation y = x + 2 considered non-proportional?

• It has a variable slope.

• It does not pass through the origin.

• It forms a curved line.

• It has no y-intercept.

What can be concluded if a line does not pass through the origin?

• The relationship is proportional.

• The line is horizontal.

• The slope is constant.

• The relationship is non-proportional.

How can you identify a non-proportional relationship without graphing?

• By examining the y-intercept.

• By checking if the line passes through the origin.

• By verifying if the line is vertical.

• By checking if the slope is zero.

What happens to the linearity of a graph if a data point is changed?

• The graph becomes non-linear.

• The slope becomes zero.

• The graph becomes vertical.

• The graph remains unchanged.

What does a constant slope indicate about a line?

• The line is vertical.

• The line is horizontal.

• The line is curved.

• The line is straight.

What is the effect of changing a data point from (2, 5) to (2, 7) on the graph?

• The graph remains proportional.

• The slope becomes constant.

• The graph becomes non-linear.

• The graph becomes a straight line.