Writing y=mx+b from verbal descriptions

Front

What does the equation y = mx + b represent?

Back

It represents the slope-intercept form of a linear equation, where m is the slope and b is the y-intercept.

Front

In the equation y = mx + b, what does 'm' represent?

Back

The slope of the line, indicating how much y changes for a unit change in x.

Front

In the equation y = mx + b, what does 'b' represent?

Back

The y-intercept, which is the value of y when x is 0.

Front

How do you write an equation from a verbal description involving a starting amount and a rate of change?

Back

Identify the starting amount as the y-intercept (b) and the rate of change as the slope (m).

Front

If a family drinks 5 bottles of water per day from a case of 48 bottles, how would you express the number of bottles left after x days?

Back

y = 48 - 5x.

Front

What is the equation for a service that charges a flat fee plus a variable rate per hour?

Back

y = mx + b, where m is the hourly rate and b is the flat fee.

Front

How would you model a situation with a startup fee and a monthly fee?

Back

Use the equation y = mx + b, where m is the monthly fee and b is the startup fee.

Front

What is the equation for babysitting if the charge is $3 plus $5 per hour?

Back

C = 5h + 3.

Front

How do you determine the total cost of renting a canoe for x hours with a flat fee?

Back

y = 30x + 20, where 30 is the hourly rate and 20 is the flat fee.

Front

If a donut shop charges $6.50 per dozen and offers a $0.75 discount, how is the equation represented?

Back

y = 6.50x - 0.75.