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 identify the y-intercept from the equation y = mx + b?

Back

In the equation y = mx + b, the y-intercept is the constant term b.

Front

What is the equation for a linear function that starts at $20 and increases by $7 for each hour worked?

Back

y = 7x + 20

Front

If a linear function is represented as y = -3x + 20, what does the -3 indicate?

Back

The -3 indicates that for every increase of 1 in x, y decreases by 3. This represents a negative slope.

Front

What is the total cost equation for a holiday meal costing $12.50 per person with a $30 delivery fee?

Back

y = 30 + 12.5x

Front

How can you determine the total cost of rides at an amusement park if the equation is y = 1.5x + 20?

Back

You can determine the total cost by substituting the number of rides (x) into the equation.

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; y does not change as x changes.

Front

What is the significance of the equation y = 20 - 3x in terms of spending?

Back

This equation shows that starting with $20, the amount decreases by $3 for each month (x) spent.