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 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 find the rate of change from a table of values?

Back

To find the rate of change, calculate the difference in y-values divided by the difference in x-values between two points.

Front

If Nate's service is described by y = 4x + 6, what is the cost when x = 2?

Back

When x = 2, y = 4(2) + 6 = 14. The cost is $14.

Front

What does it mean if one linear function is cheaper than another?

Back

It means that for the same value of x, the y-value (cost) of one function is less than the y-value of the other function.

Front

How can you compare two linear functions?

Back

You can compare their slopes and y-intercepts to determine which function increases faster and which starts at a lower value.

Front

What is the equation of a line with a slope of 3 and a y-intercept of 5?

Back

The equation is y = 3x + 5.

Front

If Rich pays a monthly fee plus a per-visit fee, what does the equation y = 3x + 10 represent?

Back

In this equation, 10 is the monthly fee (y-intercept) and 3 is the cost per visit (slope).

Front

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

Back

The rate of change can represent speed, cost per item, or any other quantity that changes in relation to another quantity.