Writing Equations from Descriptions

Front

What is the general form of a linear equation?

Back

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

Front

How do you interpret the slope in a linear equation?

Back

The slope (m) represents the rate of change of y with respect to x. It indicates how much y changes for a unit change in x.

Front

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

Back

The y-intercept (b) is the value of y when x is 0. It represents the starting point of the linear relationship on the y-axis.

Front

How can you write an equation from a word problem involving a fixed cost and a variable cost?

Back

Identify the fixed cost as the y-intercept and the variable cost per unit as the slope. The equation will be in the form y = mx + b.

Front

In the context of a budget, how would you express the remaining amount after spending a fixed amount per day?

Back

You would express it as y = initial amount - (daily spending * x), where x is the number of days.

Front

What is the significance of a negative slope in a linear equation?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship between the two variables.

Front

How do you determine the total cost of renting a car based on mileage?

Back

The total cost can be determined by the equation y = (cost per mile * miles driven) + fixed rental fee.

Front

What is the relationship between the variables in the equation y = mx + b?

Back

The relationship is linear, meaning that the change in y is proportional to the change in x.

Front

How can you identify the fixed and variable costs in a real-world scenario?

Back

Fixed costs remain constant regardless of usage (e.g., base fee), while variable costs change with usage (e.g., cost per mile or per item).

Front

What does it mean if the y-intercept is greater than zero in a cost equation?

Back

It means that there is an initial cost incurred before any variable costs are added.