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

Front

How do you write an 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 unit, x is the number of units, and b is the fixed cost.

Front

If a taxi charges a base fare plus a per-mile charge, how would you represent this mathematically?

Back

You would represent it as y = mx + b, where m is the per-mile charge, x is the number of miles, and b is the base fare.

Front

What is the equation for Bob's savings after x months if he starts with $150 and saves $40 each month?

Back

y = 40x + 150.

Front

How do you determine the total cost of a service that has both a fixed fee and a variable fee?

Back

Add the fixed fee to the product of the variable fee per unit and the number of units: y = variable fee * x + fixed fee.

Front

What is the equation for the total cost of a holiday meal for x people if it costs $12.50 per person plus a $30 delivery fee?

Back

y = 12.5x + 30.

Front

How can you identify the slope and y-intercept from an equation in slope-intercept form?

Back

In the equation y = mx + b, m is the slope and b is the y-intercept.

Front

What does it mean if the slope of a linear equation is positive?

Back

A positive slope indicates that as x increases, y also increases.