Writing and 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 y changes for a unit change in x.

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the value of y when x is 0. It represents the starting point of the function on the y-axis.

Front

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

Back

To determine the rate of change from a table, calculate the difference in y-values divided by the difference in x-values between two points.

Front

Write the linear function for Mr. Cook's savings after x weeks.

Back

y = 4x + 56, where y is the total savings and x is the number of weeks.

Front

What is the equation for the total cost of sweatshirts including shipping?

Back

y = 6.50x + 4.99, where y is the total cost and x is the number of sweatshirts.

Front

How do you compare the initial values of two linear functions?

Back

To compare initial values, look at the y-intercept (b) of each function. The function with the higher y-intercept has the greater initial value.

Front

What does it mean if two linear functions have the same slope?

Back

If two linear functions have the same slope, they have the same rate of change, meaning they increase or decrease at the same rate.

Front

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

Back

A negative slope indicates that as x increases, y decreases. This represents a decreasing relationship between the two variables.

Front

How can you identify a linear function from a graph?

Back

A linear function can be identified from a graph if the points form a straight line.