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 total cost based on hourly charges?

Back

The equation is written as y = fixed fee + (hourly rate * x), where y is the total cost, the fixed fee is the initial charge, and x is the number of hours.

Front

What is the equation for Bob's savings after x months if he saves a fixed amount each month?

Back

The equation is y = 40x + 150, where y is the total amount in savings, 40 is the amount saved each month, and 150 is the initial amount.

Front

How do you represent a situation where a person descends from a height?

Back

The equation is y = initial height - (descent rate * x), where y is the height after x minutes, initial height is the starting point, and descent rate is how fast they descend.

Front

What is the equation for a lunch bill involving multiple items?

Back

The equation can be represented as ax + by = total, where a and b are the prices of the items, x and y are the quantities, and total is the final bill.

Front

What does it mean if a situation has a y-intercept?

Back

A y-intercept indicates a starting value in a situation, such as an initial amount before any changes occur.

Front

How do you determine the total cost of renting a car for x hours?

Back

Use the equation y = 25.5 + 8.5x, where 25.5 is the rental fee and 8.5 is the hourly charge.

Front

What is the significance of the coefficients in a linear equation?

Back

Coefficients represent the rate of change or the amount associated with each variable in the equation.