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 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. It is found by dividing one quantity by the other (k = y/x).

Front

How do you find the slope of a linear equation?

Back

The slope (m) of a linear equation in the form y = mx + b is the coefficient of x. It represents the rate of change of y with respect to x.

Front

What does the y-intercept represent in a linear equation?

Back

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

Front

If a car travels 60 miles in 1 hour, how far will it travel in 3 hours?

Back

180 miles (60 miles/hour * 3 hours = 180 miles).

Front

What is the equation of a line with a slope of 2 and a y-intercept of 3?

Back

y = 2x + 3.

Front

How do you determine if a relationship is proportional?

Back

A relationship is proportional if the ratio of the two quantities is constant. This can be checked by finding the constant of proportionality.

Front

What is the formula to calculate the distance traveled at a constant speed?

Back

Distance = Speed × Time.

Front

If the equation of a line is y = 4x - 2, what is the slope?

Back

The slope is 4.

Front

What does it mean if a linear relationship is nonproportional?

Back

A nonproportional linear relationship means that the ratio of the two quantities is not constant, and the line does not pass through the origin.