Comparing Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function. It indicates how much the y-value changes for a one-unit increase in the x-value.

Front

How do you find the slope from a graph?

Back

To find the slope from a graph, select two points on the line, calculate the rise (change in y) and run (change in x), and then use the formula slope = rise/run.

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

Front

How can you determine if two linear functions have the same slope?

Back

Two linear functions have the same slope if their equations have the same value of m in the slope-intercept form y = mx + b.

Front

What is the rate of change in a real-world context?

Back

The rate of change in a real-world context refers to how one quantity changes in relation to another, often expressed as a cost per unit, speed, or growth rate.

Front

How do you calculate the rate of change from a table of values?

Back

To calculate the rate of change from a table, take two points (x1, y1) and (x2, y2) and use the formula: rate of change = (y2 - y1) / (x2 - x1).

Front

What is the significance of a negative slope?

Back

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

Front

What does it mean if two functions are parallel?

Back

Two functions are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.

Front

How do you interpret the slope in a cost function?

Back

In a cost function, the slope represents the cost per unit of the item being measured, indicating how much the total cost increases with each additional unit.