Linear Equation 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 of 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 C = variable_cost * m + flat_fee.

Front

In the equation h = 1.4t + 1.9, what does the 1.4 represent?

Back

The 1.4 represents the cost increase per topping added to the hamburger.

Front

How can you represent a situation where a quantity decreases over time in a linear equation?

Back

Use a negative slope. For example, if a person spends money each month, the equation can be written as y = -mx + initial_amount.

Front

What does the equation y = -3x + 20 represent in a real-world context?

Back

It represents a situation where Sandra starts with $20 and spends $3 each month, decreasing her balance over time.

Front

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

Back

The initial fee is the fixed cost incurred before any variable costs are added. It is represented by the y-intercept in the equation.

Front

How do you determine the total cost from a linear equation involving a service charge?

Back

Add the flat fee to the product of the variable cost per unit and the number of units (m). For example, C = 8m + 50.

Front

What does the equation y = 15x + 80 indicate about membership growth?

Back

It indicates that the fitness club starts with 80 members and gains 15 new members each month.