Modeling Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that models a straight line, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear equation?

Back

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

Front

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

Back

The y-intercept (b) represents the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

How do you write an equation for a total cost scenario?

Back

To write an equation for a total cost scenario, identify the fixed costs and variable costs, then express the total cost as the sum of these costs, typically in the form y = mx + b.

Front

What is the significance of the delivery fee in a cost equation?

Back

The delivery fee is a fixed cost that does not change with the number of items or people, and it is represented as the constant term in the equation.

Front

How do you determine the total cost for multiple items in a linear cost equation?

Back

To determine the total cost for multiple items, multiply the cost per item by the number of items and add any fixed costs.

Front

What is the equation for total expenses if you have a fixed entry fee and a variable cost per item?

Back

The equation is typically in the form y = mx + b, where m is the variable cost per item, x is the number of items, and b is the fixed entry fee.

Front

How can you represent savings over time with a linear equation?

Back

Savings over time can be represented with the equation y = mx + b, where m is the amount saved per time period, x is the number of time periods, and b is the initial amount saved.

Front

What is the relationship between the number of minutes used and the total cost in a phone service scenario?

Back

The total cost is a linear function of the number of minutes used, represented by the equation c = 0.12m + 8, where 0.12 is the cost per minute and 8 is the monthly service fee.

Front

How do you solve for x in a linear equation?

Back

To solve for x in a linear equation, isolate x on one side of the equation by performing inverse operations on both sides.