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 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 is the point where the line crosses the y-axis.

Front

How do you write a linear equation from a word problem?

Back

Identify the variables, determine the fixed costs and variable costs, and then express the relationship in the form of y = mx + b.

Front

If a shirt costs $8 and there is a $15 setup fee, what is the equation for the total cost (y) for x shirts?

Back

y = 8x + 15.

Front

How do you calculate the total cost for 50 shirts if the equation is y = 8x + 15?

Back

Substitute x with 50: y = 8(50) + 15 = 400 + 15 = 415.

Front

What is 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 find the total cost for 2.5 hours of labor if the plumber charges $50 for a house call and $25 per hour?

Back

Total cost = $50 + ($25 * 2.5) = $50 + $62.50 = $112.50.

Front

What is the linear equation for the cost of business cards if 200 cards cost $23 and 500 cards cost $35?

Back

y = 0.04x + 15.

Front

How do you determine the fixed rate from the cost of renting a gym for different numbers of students?

Back

Set up equations based on the number of students and total cost, then solve for the fixed rate.