Linear Functions Practice

Front

What is the slope-intercept form of a linear equation?

Back

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

Front

If the slope of a line is 3 and the y-intercept is 6, what is the equation of the line?

Back

y = 3x + 6

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is.

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 of b in the slope-intercept form.

Front

How do you find the cost function for a service with a fixed fee and a variable rate?

Back

The cost function can be expressed as C(x) = fixed fee + (variable rate * x), where x is the number of units (e.g., hours of service).

Front

Calculate P(4) if P(x) = 50 + 12x.

Back

P(4) = 50 + 12(4) = 50 + 48 = 98.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, characterized by a constant rate of change.

Front

How can you determine if a function is linear or nonlinear?

Back

A function is linear if it can be expressed in the form y = mx + b. If it cannot, it is nonlinear.

Front

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

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

If a table shows a constant change in y for a constant change in x, what type of function is it?

Back

It is a linear function.