Linear Relationships Prep

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph. It can be expressed in the form of an equation, typically y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the constant of proportionality?

Back

The constant of proportionality is the constant value (k) that relates two proportional quantities. In the equation y = kx, k represents the constant of proportionality.

Front

How do you find the constant of proportionality from a word problem?

Back

To find the constant of proportionality, divide the total amount by the quantity. For example, if 14 gallons of gas cost $48.86, the constant of proportionality is $48.86 / 14 = $3.49.

Front

What does the slope of a linear equation represent?

Back

The slope of a linear equation represents the rate of change between the two variables. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

What is a nonproportional relationship?

Back

A nonproportional relationship is a relationship between two variables that does not have a constant ratio. It can be represented by a linear equation that includes a y-intercept other than zero.

Front

Given the equation y = 3x + 4, what is the slope?

Back

The slope of the equation y = 3x + 4 is 3.

Front

If a table shows a linear relationship, how can you extend it?

Back

To extend a table showing a linear relationship, use the slope to calculate the next values based on the previous ones. For example, if the slope is 3, add 3 to the previous y-value for each increase in x.

Front

What is the formula to calculate the distance traveled in a linear relationship?

Back

The formula to calculate distance in a linear relationship is d = rt, where d is distance, r is rate (slope), and t is time.

Front

How do you determine if a relationship is proportional or nonproportional?

Back

A relationship is proportional if it can be expressed as y = kx (where k is a constant) and passes through the origin (0,0). If it has a y-intercept other than zero, it is nonproportional.