Writing 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 y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear function?

Back

The slope (m) represents the rate of change of the function. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept (b) in a linear function?

Back

The y-intercept (b) is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

How do you write the equation of a line given a slope and a y-intercept?

Back

The equation can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the equation for the total cost of renting a snowboard for x hours if the cost is $15 per hour plus a $25 rental fee?

Back

y = 15x + 25.

Front

How do you represent a situation where a delivery fee is added to a per-person cost?

Back

The total cost can be represented as y = fixed fee + (cost per person * number of people).

Front

If a man is descending from a height of 100 feet at a rate of 30 feet per minute, how would you express this as a linear equation?

Back

y = -30x + 100.

Front

What is the equation for the total cost of a holiday meal for x people if it costs $12.50 per person plus a $30 delivery fee?

Back

y = 30 + 12.5x.

Front

How do you determine the total cost of picking fruit if there is a base charge and a per-pound charge?

Back

The total cost can be expressed as y = base charge + (cost per pound * pounds picked).

Front

What does it mean if the slope of a linear function is negative?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship.