#linearfunctions

[enzoexposyto]

Equations for the Family

[enzoexposyto]

Equations for the Family

[linearworld]

Nuts and Bolts

The distance a bolt protrudes past the edge of a nut is a linear function of the number of revolutions through which the bolt is turned.

The slope is the distance covered per revolution (in cm per turn).

The y-intercept is the opposite of the "length" of the nut.

The x-intercept is the number of turns required to make the bolt just flush with the other end of the nut.

Suppose the nut is 1 cm long and the bolt travels .4 cm per turn.

[linearworld]

Snowblower Business

The profit you make after buying a snowblower and paying for a business license is a linear function of the number of jobs you get. The slope is the average amount you charge per job. The y-intercept is the starting profit deficit from the buying the blower and the license. The x-intercept is the number of jobs to break even. Suppose the blower and license are $750 and you charge $45 per job.

[linearworld]

Sharpening Pencils

The change in the length of a pencil being sharpened is a linear function of and the number of revolutions the shaving mechanism has undergone.

The slope is the length of pencil shredded away per crank. The y-intercept is the pencil's original length,

The original length could be about 18 cm, shredding away at .1 cm per crank.

[linearworld]

Gas and Cigarettes

Someone pulls into a gas station to buy a carton of cigarettes and to fill his tank. The price paid is a linear function of the number of gallons he buys. The slope is the price of a gallon of gas. The y-intercept is the cost of the carton of cigarettes.

A carton of cigarettes could be $48, and a gallon of gas could be $3.26 or so.