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 f(x) = 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 output (y) changes for a unit change in the input (x).

Front

How do you find the value of a linear function at a specific point?

Back

To find the value of a linear function at a specific point, substitute the x-value into the function and solve for f(x).

Front

What is the y-intercept of a linear function?

Back

The y-intercept of a linear function is the point where the graph intersects the y-axis. It is the value of f(x) when x = 0.

Front

If g(x) = 9x + 24, what is g(3)?

Back

g(3) = 9(3) + 24 = 27 + 24 = 51.

Front

What is the difference between linear and quadratic functions?

Back

Linear functions have a constant rate of change and are represented by straight lines, while quadratic functions have a variable rate of change and are represented by parabolas.

Front

How do you determine 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 does it mean if the slope of a line is negative?

Back

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

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

If f(x) = 2x + 1, what is f(1)?

Back

f(1) = 2(1) + 1 = 2 + 1 = 3.