Key Features of 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 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 y changes for a unit change in x.

Front

How do you find the y-intercept of a linear equation?

Back

To find the y-intercept of a linear equation, set x to 0 and solve for y.

Front

What is the y-intercept of the equation 4x + 2y = -12?

Back

The y-intercept is -6.

Front

What is the x-intercept of a function?

Back

The x-intercept is the point where the graph of the function crosses the x-axis, which occurs when y = 0.

Front

How do you find the x-intercept of a linear equation?

Back

To find the x-intercept of a linear equation, set y to 0 and solve for x.

Front

What is the x-intercept of the ordered pairs (8,10), (3,-4), (0,8), (4,-3), (9,0)?

Back

The x-intercept is (9,0).

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant of the line.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the line.

Front

What does a slope of zero indicate about a linear function?

Back

A slope of zero indicates that the function is constant, meaning y does not change as x changes.