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 represents the rate of change of the function. It indicates how much y changes for a unit change in x.

Front

How do you determine the slope from an equation in slope-intercept form?

Back

In the equation y = mx + b, the slope is the coefficient m of x.

Front

What is the y-intercept of a linear function?

Back

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

Front

How do you compare the slopes of two linear functions?

Back

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

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 and will never intersect.

Front

What is the formula to calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

How can you find the y-intercept from a linear equation in standard form?

Back

To find the y-intercept from the standard form Ax + By = C, set x = 0 and solve for y.

Front

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

Back

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

Front

What is the significance of the y-intercept in real-world applications?

Back

The y-intercept often represents the starting value or initial condition in real-world scenarios, such as cost or population.