Math 180 Proportional and Linear Relationships B2

Front

What is a proportional relationship?

Back

A proportional relationship is a relationship between two quantities where the ratio of one quantity to the other is constant.

Front

What does the equation y = kx represent?

Back

This equation represents a direct variation where y varies directly with x, and k is the constant of proportionality.

Front

If y = 25x, what does the number 25 represent?

Back

The number 25 represents the rate at which y increases for each unit increase in x.

Front

Why can't Justin purchase 2.2 paintbrushes?

Back

Because paintbrushes can only be bought in whole numbers, not fractions.

Front

What is the solution to the equation 410 = 25x?

Back

The solution is x = 16.4, meaning Max can afford 16 full canvases.

Front

How do you find the number of items you can buy with a budget?

Back

Use the equation y = px, where p is the price per item and x is the number of items.

Front

What does the slope of a line in a graph represent in a proportional relationship?

Back

The slope represents the constant rate of change between the two variables.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is zero, indicating the starting point of the relationship.

Front

How can you determine if a relationship is linear?

Back

A relationship is linear if it can be represented by a straight line on a graph.

Front

What is the equation for a proportional relationship if the constant of proportionality is 1.2?

Back

The equation is y = 1.2x.