Comparing Linear Functions

Front

What is 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 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 compare the slopes of two linear functions?

Back

To compare the slopes, look at the coefficients of x in their equations. The function with the larger coefficient has a greater slope.

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

If two linear functions have the same slope, what can be said about their graphs?

Back

If two linear functions have the same slope, their graphs are parallel to each other.

Front

What does it mean if a linear function has a negative slope?

Back

A negative slope means that as the x-value increases, the y-value decreases. The graph of the function will slant downwards from left to right.

Front

What does it mean if a linear function has a positive slope?

Back

A positive slope means that as the x-value increases, the y-value also increases. The graph of the function will slant upwards from left to right.

Front

How can you determine which of two linear functions is cheaper at a given point?

Back

To determine which function is cheaper at a given point, substitute the x-value into both equations 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 Randy charges $400 per month and increases the charge by $25, what is the new monthly charge?

Back

The new monthly charge is $425.