Comparing Linear Functions

Front

What is the slope of a linear function?

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

What does a higher slope indicate in a linear function?

Back

A higher slope indicates a steeper line, meaning the function increases or decreases more rapidly.

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

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

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 as (0, b) in the equation y = mx + b.

Front

How do you determine which of two linear functions has a greater slope?

Back

Compare the coefficients of x in the equations. The function with the larger coefficient has the greater slope.

Front

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

Back

If two linear functions have the same slope, they are parallel and will never intersect.

Front

What is the equation of a line in slope-intercept form?

Back

The slope-intercept form of a line is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you tell if a linear function is increasing or decreasing?

Back

A linear function is increasing if the slope is positive and decreasing if the slope is negative.

Front

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

Back

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

Front

If a linear function has a slope of 0, what does that indicate?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.