Rate of Change & Word Problems

Front

What is the equation for a linear relationship where a flat fee of $3 is charged plus $5 per hour?

Back

y = 5x + 3, where y is the total cost and x is the number of hours.

Front

How do you represent the total cost of waffle ice cream cones with a base price and additional cost per scoop?

Back

y = 0.60x + 1.85, where y is the total cost and x is the number of scoops.

Front

What is the equation for the total cost of sandwiches if each sandwich costs $7?

Back

C = 7S, where C is the total cost and S is the number of sandwiches.

Front

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

Back

The y-intercept represents the value of y when x is 0, indicating the starting value or fixed cost.

Front

How do you determine which linear equation has the greatest rate of change?

Back

The rate of change is determined by the slope of the line; the greater the slope, the greater the rate of change.

Front

What is the slope in the equation y = mx + b?

Back

The slope (m) represents the rate of change of y with respect to x.

Front

In the context of word problems, what does 'rate of change' refer to?

Back

Rate of change refers to how much one quantity changes in relation to another quantity.

Front

How can you identify the fixed cost in a word problem involving linear equations?

Back

The fixed cost is the value of y when x is 0, often represented by the y-intercept in the equation.

Front

What is the significance of the coefficients in a linear equation?

Back

Coefficients represent the rate of change or the cost per unit in application-based problems.

Front

How do you convert a word problem into a linear equation?

Back

Identify the variables, fixed costs, and rates of change, then formulate the equation based on the relationships described.