Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in 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 function. It indicates how much the y-value changes for a unit change in the x-value.

Front

What is the y-intercept of a linear function?

Back

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

Front

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

Back

The cost function can be expressed as C(x) = base fee + (variable fee per unit * x), where x is the number of units.

Front

Calculate P(4) for the function P(x) = 50 + 12x.

Back

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

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is 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?

Back

The equation is y = 3x + 6.

Front

How do you determine if a graph is linear?

Back

A graph is linear if it forms a straight line when plotted on a coordinate plane.

Front

Write the linear function for Jerome's savings after x months if he starts with $150 and saves $40 per month.

Back

J(x) = 40x + 150.

Front

What is the cost function for the Roaming Cell Phone Company?

Back

C(x) = 2x + 15, where x is the number of minutes used.