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 y-intercept represent in a linear equation?

Back

The y-intercept is the value of y when x is 0. It represents the starting point of a linear relationship on a graph.

Front

How do you write an equation for a total cost that includes a fixed fee and a variable cost?

Back

The equation is written as y = fixed fee + (variable cost per unit * number of units).

Front

If a meal costs $12.50 per person and has a delivery fee of $30, how would you express the total cost for x people?

Back

The total cost can be expressed as y = 30 + 12.5x.

Front

What is the formula to find the remaining balance on a gift card after spending a certain amount each month?

Back

The formula is y = initial amount - (amount spent per month * number of months).

Front

In the equation y = -3x + 20, what does the -3 represent?

Back

The -3 represents the amount of money spent each month, indicating a decrease in the balance.

Front

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

Back

The slope indicates the rate of change of y with respect to x. It shows how much y increases or decreases for each unit increase in x.

Front

How do you determine the cost per unit from a total cost equation?

Back

To find the cost per unit, identify the coefficient of x in the equation, which represents the variable cost.

Front

What does it mean if a linear equation has a positive slope?

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship between the two variables.

Front

What is the equation for total charges if a rental service charges a flat fee plus an hourly rate?

Back

The equation is y = flat fee + (hourly rate * number of hours).