8.5I-Writing Equations in the Form y=mx+b (Verbal)

Front

What does the equation y = mx + b represent?

Back

It represents a linear equation where y is the dependent variable, m is the slope, x is the independent variable, and b is the y-intercept.

Front

What is the slope in the equation y = -25x + 120?

Back

The slope (m) is -25, indicating that for every 1 unit increase in x, y decreases by 25.

Front

What does the y-intercept represent in the equation y = mx + b?

Back

The y-intercept (b) is the value of y when x = 0, representing the starting point of the line on the y-axis.

Front

How do you identify the slope from the equation y = 5 + 3x?

Back

The slope is the coefficient of x, which is 3 in this case.

Front

What is the equation for a plant that starts at 5 cm and grows 3 cm per month?

Back

The equation is y = 5 + 3x, where y is the height after x months.

Front

If a tank releases water at a rate of 25 gallons per minute, what is the equation for the amount of water left after x minutes if it starts with 120 gallons?

Back

The equation is y = 120 - 25x.

Front

What does the equation y = 30x + 20 represent in a canoe rental scenario?

Back

It represents the total cost (y) of renting a canoe for x hours, including a $20 transportation fee.

Front

How do you write an equation for a streaming service that charges $15 annually plus $3 per movie?

Back

The equation is y = 3x + 15, where y is the total cost for renting x movies.

Front

What is the significance of the negative slope in the equation y = -3,000x + 15,000?

Back

A negative slope indicates that as x increases, y decreases, showing a decline in the number of tickets remaining.

Front

What is the general form of a linear equation?

Back

The general form is y = mx + b, where m is the slope and b is the y-intercept.