Modeling Linear Word Problems

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 the slope in a linear equation represent?

Back

The slope 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 is the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is 0. It represents the starting point of the line on the y-axis.

Front

How do you write an equation for a word problem involving a flat fee and a variable cost?

Back

Identify the flat fee and the variable cost per unit. The equation will be in the form: Total Cost = Flat Fee + (Variable Cost per Unit * Number of Units).

Front

Write the equation for the total cost of towing a vehicle for m miles if the flat fee is $50 and the cost per mile is $8.

Back

C = 8m + 50

Front

How do you represent a total cost that includes a delivery fee and a cost per person?

Back

The equation will be: Total Cost = Delivery Fee + (Cost per Person * Number of People).

Front

Write the equation for the total cost of a holiday meal for x people if the cost is $12.50 per person and there is a $30 delivery fee.

Back

y = 30 + 12.5x

Front

How do you express savings over time in an equation?

Back

Identify the initial amount and the amount saved per time period. The equation will be: Total Savings = Initial Amount + (Amount Saved per Month * Number of Months).

Front

Write the equation for Bob's savings after x months if he starts with $150 and saves $40 each month.

Back

y = 40x + 150

Front

How do you model a situation where a quantity decreases over time?

Back

Identify the initial quantity and the amount decreased per time period. The equation will be: Remaining Quantity = Initial Quantity - (Amount Decreased per Day * Number of Days).