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 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 unit change 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 from a word problem involving a flat fee and a variable cost?

Back

Identify the fixed cost and the variable cost, then express the total cost as an equation: Total Cost = Fixed Cost + (Variable Cost per unit * Number of units).

Front

Write the equation for a service that charges a flat fee of $50 plus $8 per mile.

Back

C = 8m + 50

Front

How do you convert a word problem into slope-intercept form?

Back

Identify the initial value (y-intercept) and the rate of change (slope), then write the equation as y = mx + b.

Front

What is the total cost for renting a vehicle for 100 miles if the rate is $30 per day plus $0.25 per mile?

Back

Total Cost = $30 + ($0.25 * 100) = $30 + $25 = $55.

Front

How do you represent a situation where membership increases over time with a linear equation?

Back

Identify the initial number of members and the rate of increase, then write the equation as y = mx + b, where m is the rate of increase and b is the initial number.

Front

Write the equation for a fitness club that starts with 80 members and increases by 15 members each month.

Back

y = 15x + 80

Front

What is the equation for a gym that charges a one-time fee and a monthly fee?

Back

Total Cost = One-time Fee + (Monthly Fee * Number of Months).