Writing Equations for Real-World Scenarios

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does 'initial value' mean in a real-world scenario?

Back

The initial value is the starting point or the value at time t=0 in a situation, often represented as a constant in an equation.

Front

How do you represent a decrease in a quantity over time in an equation?

Back

A decrease can be represented by subtracting a product of the rate of decrease and time from the initial value, e.g., D = initial value - rate * t.

Front

How do you represent an increase in a quantity over time in an equation?

Back

An increase can be represented by adding a product of the rate of increase and time to the initial value, e.g., B = initial value + rate * t.

Front

What is the formula for calculating total cost with a fixed fee and a variable cost?

Back

The total cost can be calculated using the formula C = fixed fee + (variable cost per unit * number of units).

Front

In the equation F = 3 + 1.5m, what does each term represent?

Back

F represents the total fare, 3 is the base fare, 1.5 is the cost per mile, and m is the number of miles traveled.

Front

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

Back

The slope indicates the rate of change of the dependent variable with respect to the independent variable, showing how much y changes for a unit change in x.

Front

How do you write an equation for a situation where a quantity is being filled at a constant rate?

Back

You write the equation as Q = initial amount + (rate * time), where Q is the quantity at time t.

Front

What does the variable 't' typically represent in equations related to time?

Back

In these equations, 't' usually represents time, often measured in minutes, hours, or years.

Front

How can you identify the initial value in a word problem?

Back

The initial value is often explicitly stated as the starting amount or can be inferred from the context of the problem.