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 does the y-intercept (b) represent in a linear function?

Back

The y-intercept (b) is the value of y when x is 0. It represents the starting point of the function on the y-axis.

Front

How do you write the equation of a linear function from a word problem?

Back

Identify the fixed costs (y-intercept) and the variable costs (slope) from the problem, then use the form y = mx + b.

Front

If Heather charges $12 per hour and $5 to reserve, what is the equation for her total charge?

Back

y = 12x + 5.

Front

If Bob saves $40 per month starting with $150, what is the equation for his savings?

Back

y = 40x + 150.

Front

What is the equation for a donut shop that charges $6.50 per dozen and gives a $0.75 discount?

Back

y = 6.50x - 0.75.

Front

If Randy increases his rent from $400 to $425, what is the new equation for his tenants?

Back

y = 425x + 600.

Front

What is the total cost equation for renting golf clubs and playing a round of golf?

Back

T = 15 + 25r.

Front

What is the significance of the term 'fixed cost' in a linear function?

Back

Fixed cost refers to the cost that does not change with the level of output or activity, represented by the y-intercept in the equation.