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 situation involving a fixed cost and a variable cost?

Back

The equation can be written as y = fixed cost + (variable cost per unit * x), where x is the number of units.

Front

If Sonya has $40 and spends $2 each day, how can we express her remaining balance after x days?

Back

y = 40 - 2x.

Front

How do you find the break-even point in a word problem involving two different pricing structures?

Back

Set the total costs of both options equal to each other and solve for the variable (usually time or quantity).

Front

What is the total cost equation for Joe’s Canoes if it charges $20 plus $4 per hour?

Back

y = 20 + 4x.

Front

How do you determine the number of items sold if you know the total revenue and the price per item?

Back

Divide the total revenue by the price per item: Number of items = Total Revenue / Price per item.

Front

What is the equation for Sandra's iTunes gift card balance after x months if she spends $3 each month?

Back

y = -3x + 20.

Front

How can you represent a situation where a rental fee is charged plus a variable hourly rate?

Back

The equation can be written as y = fixed fee + (hourly rate * x).