Linear Equations 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 variable 'y' represent in a linear equation?

Back

In a linear equation, 'y' typically represents the dependent variable, which is the output or total cost in word problems.

Front

What does the variable 'x' represent in a linear equation?

Back

In a linear equation, 'x' typically represents the independent variable, which is the input or quantity of items in word problems.

Front

How do you write a linear equation for a situation with a fixed cost and a variable cost?

Back

The equation is written as y = mx + b, where m is the variable cost per item, x is the number of items, and b is the fixed cost.

Front

What is the slope in a linear equation?

Back

The slope (m) in a linear equation represents the rate of change of y with respect to x, indicating how much y changes for a unit change in x.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept (b) is the value of y when x is 0. It represents the starting value or fixed cost in word problems.

Front

How do you interpret the y-intercept in a real-world context?

Back

The y-intercept represents the initial cost or starting amount before any variable costs are added.

Front

What is the equation for total cost if a service charges a flat fee plus a per-hour rate?

Back

The equation is y = b + mx, where b is the flat fee, m is the per-hour rate, and x is the number of hours.

Front

If a T-shirt costs $8 each and there is a $25 design fee, what is the equation for total cost?

Back

The equation is y = 8x + 25, where y is the total cost and x is the number of T-shirts.

Front

How do you find the total cost for renting a boat with a deposit and hourly rate?

Back

Use the equation C = deposit + (hourly rate * hours), where C is total cost.