Rate of Change and Initial Value (Verbal/Equations)

Front

What is the rate of change in a linear equation?

Back

The rate of change in a linear equation represents the slope, which indicates how much the dependent variable (y) changes for a unit change in the independent variable (x).

Front

How do you identify the slope from the equation y = mx + b?

Back

In the equation y = mx + b, 'm' represents the slope, which is the rate of change of y with respect to x.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the value of y when x is 0, representing the starting point of the linear relationship.

Front

Write the equation for a situation where there is a fixed cost and a variable cost per month.

Back

The equation can be written as y = mx + b, where 'm' is the variable cost per month, and 'b' is the fixed cost.

Front

In the equation y = 12x + 35, what does 12 represent?

Back

In the equation y = 12x + 35, 12 represents the rate of change or the monthly cost associated with the gym membership.

Front

If a pool has 78 gallons of water and is filled at a rate of 3 gallons per minute, what is the initial amount of water in the pool?

Back

The initial amount of water in the pool is 78 gallons, which is the y-intercept in this context.

Front

How can you determine the slope from a word problem involving costs?

Back

The slope can be determined by identifying the variable cost per unit (e.g., per month) in the context of the problem.

Front

What is the significance of the initial value in a real-world application problem?

Back

The initial value represents the starting point or fixed cost before any variable costs are added.

Front

How do you find the total cost after a certain number of months if you know the monthly rate and initial fee?

Back

You can find the total cost by using the equation y = mx + b, where 'm' is the monthly rate, 'x' is the number of months, and 'b' is the initial fee.

Front

What is the slope in the equation y = 8x + 6?

Back

The slope in the equation y = 8x + 6 is 8, indicating the rate of change of y with respect to x.