Linear Functions

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.

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.

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

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

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

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

The equation is y = 3x + 6.

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

J(x) = 40x + 150.

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