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 does the constant of proportionality represent?

Back

The constant of proportionality is the ratio between two proportional quantities. In a linear relationship, it represents the slope of the line, indicating how much one variable changes in relation to another.

Front

How do you find the constant of proportionality from a given cost and quantity?

Back

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

Front

What is the slope in a linear equation?

Back

The slope in a linear equation (y = mx + b) is the coefficient 'm' that indicates the steepness of the line. 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 is the value of y when x is 0 in the equation y = mx + b. It represents the point where the line crosses the y-axis.

Front

How can you determine if a relationship is proportional?

Back

A relationship is proportional if the ratio of the two quantities remains constant. This can be checked by calculating the constant of proportionality and ensuring it is the same for all pairs of values.

Front

What is the equation of a non-proportional linear relationship?

Back

A non-proportional linear relationship can be expressed in the form y = mx + b, where b is not equal to 0. This indicates that the line does not pass through the origin.

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 additional values. For example, if the slope is 3 and the last value is 10, the next value can be found by adding 3 to the previous output.

Front

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

Back

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

Front

How do you interpret the slope of a line in a real-world context?

Back

The slope of a line in a real-world context represents the rate of change between two quantities. For example, in a distance-time graph, the slope indicates how fast an object is moving.