STAAR Released Questions: Slope & Functions

Front

What is the slope of a linear function?

Back

The slope of a linear function represents the rate of change of the function. It is calculated as the change in the y-value divided by the change in the x-value (rise/run).

Front

Define a linear function.

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

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

Front

How do you determine if a relationship is proportional?

Back

A relationship is proportional if it can be expressed as y = kx, where k is a constant. This means that as x increases, y increases at a constant rate.

Front

What is the equation of a line with a negative slope?

Back

An equation of a line with a negative slope can be written as y = mx + b, where m is negative. This indicates that as x increases, y decreases.

Front

Explain the concept of a function.

Back

A function is a relation that assigns exactly one output (y) for each input (x). In other words, for every x-value, there is one corresponding y-value.

Front

What is a constant rate of change?

Back

A constant rate of change means that the change in y for each unit change in x is the same throughout the function. This is characteristic of linear functions.

Front

How can you identify a function from a set of ordered pairs?

Back

To identify a function from a set of ordered pairs, ensure that no x-value is repeated with a different y-value. Each x must correspond to exactly one y.

Front

What does it mean for y to be a function of x?

Back

It means that for each value of x, there is a unique value of y. This relationship can be expressed as y = f(x).

Front

What is the significance of the slope in real-world situations?

Back

The slope in real-world situations often represents a rate, such as speed, cost per item, or growth rate, indicating how one quantity changes in relation to another.