Evaluate 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 (m) 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

What is the y-intercept of a linear function?

Back

The y-intercept (b) of a linear function is the value of the function when x = 0. It is the point where the line crosses the y-axis.

Front

How do you evaluate a linear function at a specific point?

Back

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

Front

Evaluate f(x) = -3x + 3 at x = 0.

Back

f(0) = -3(0) + 3 = 3.

Front

Evaluate y = 6x + 22 at x = -2.

Back

y = 6(-2) + 22 = -12 + 22 = 10.

Front

Evaluate f(x) = 2x + 3 at x = -4.

Back

f(-4) = 2(-4) + 3 = -8 + 3 = -5.

Front

What is the value of f(1) for the function f(x) = 2x + 3?

Back

f(1) = 2(1) + 3 = 2 + 3 = 5.

Front

If f(x) = mx + b, what do m and b represent?

Back

m represents the slope of the line, and b represents the y-intercept.

Front

How can you find the x-intercept of a linear function?

Back

To find the x-intercept, set f(x) = 0 and solve for x.