Comparing Linear Functions (8.F.2)

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in 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 represents the rate of change of the function, indicating how much y changes for a unit change in x.

Front

How do you compare the rates of change of two linear functions?

Back

You compare the slopes of the functions; the function with the greater slope has a higher rate of change.

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the value of y when x is 0, representing where the line crosses the y-axis.

Front

If a linear function has a slope of 5, what does this mean in a real-world context?

Back

It means that for every 1 unit increase in x, y increases by 5 units.

Front

How can you determine which of two linear functions is greater at a specific x-value?

Back

Substitute the x-value into both functions and compare the resulting y-values.

Front

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

Back

The equation is y = 3x + 2.

Front

If Alicia does 5 more jumping jacks per minute than Melissa, how can this be represented in a linear equation?

Back

If Melissa's rate is m, then Alicia's rate can be expressed as m + 5.

Front

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

Back

It helps to understand how one quantity changes in relation to another, such as speed, cost, or growth.

Front

How do you find the cost of services given a linear equation?

Back

Substitute the number of services (x) into the equation to find the total cost (y).