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

Write the equation for a linear function with a slope of 3 and a y-intercept of 2.

Back

y = 3x + 2

Front

If a linear function has a slope of -4, what does this indicate about the graph?

Back

A slope of -4 indicates that the graph of the function decreases as x increases, meaning it goes downwards from left to right.

Front

How do you find the total cost if a service charges a fixed fee plus a variable fee per hour?

Back

The total cost can be represented by the equation y = mx + b, where m is the variable fee per hour, x is the number of hours, and b is the fixed fee.

Front

What is the equation for a situation where a person has $50 and spends $5 each week?

Back

y = -5x + 50, where y is the amount of money left after x weeks.

Front

How do you interpret the y-intercept in a real-world context?

Back

The y-intercept represents the starting value or initial condition before any changes occur.

Front

Write an equation for a linear function that represents a person earning $10 per hour starting with $30.

Back

y = 10x + 30

Front

What does it mean if a linear function has a slope of 0?

Back

A slope of 0 means that the function is constant; the value of y does not change regardless of x.