Linear Functions Flashcard

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane 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 line represent?

Back

The slope of a line represents the rate of change of the y-coordinate with respect to the x-coordinate. It indicates how steep the line is and the direction it goes (positive, negative, zero, or undefined).

Front

How do you convert a linear equation to slope-intercept form?

Back

To convert a linear equation to slope-intercept form (y = mx + b), isolate y on one side of the equation.

Front

What is the slope-intercept form of the equation 4x + y = 10?

Back

y = -4x + 10.

Front

What are the first four terms of the sequence defined by a1 = 5, an = an-1 + 4?

Back

5, 9, 13, 17.

Front

What type of slope does a horizontal line have?

Back

A horizontal line has a slope of zero.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

How do you find the cost function for a pizza with a base price and additional toppings?

Back

The cost function can be expressed as C(x) = base price + (cost per topping * number of toppings). For example, C(x) = 6 + 1.5x.

Front

If a pizza place charges $6 for a medium pizza plus $1.50 per topping, what is the cost for 5 toppings?

Back

C(5) = 6 + 1.5(5) = $13.50.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-value increases, the y-value also increases.