Test - 12 Weeks

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function represents how much the output value (y) changes for a unit change in the input value (x). It is often represented by the slope of the line.

Front

How do you calculate the constant of proportionality?

Back

The constant of proportionality can be calculated by dividing the output value by the input value in a proportional relationship. It represents the ratio between the two quantities.

Front

What is the formula for slope in a linear equation?

Back

The slope (m) of a linear equation is calculated as m = (change in y) / (change in x). It indicates the steepness and direction of the line.

Front

Write the equation for a linear function given a slope and a y-intercept.

Back

The equation of a linear function can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for y to vary directly as x?

Back

When y varies directly as x, it means that y is proportional to x, and can be expressed as y = kx, where k is the constant of proportionality.

Front

How do you find the total cost of renting a boat given a deposit and hourly rate?

Back

The total cost can be calculated using the equation y = mx + b, where m is the hourly rate, x is the number of hours, and b is the deposit fee.

Front

What is the significance of a negative slope in a linear function?

Back

A negative slope indicates that as the input value (x) increases, the output value (y) decreases, showing an inverse relationship between the two variables.

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, meaning it has a constant rate of change.

Front

What is the relationship between slope and rate of change?

Back

The slope of a line is a specific measure of the rate of change, indicating how much y changes for a unit change in x.

Front

How do you interpret the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is zero. It represents the starting point of the linear function on the y-axis.