Linear equation word problems

Front

What is a linear equation?

Back

A linear equation is an equation that represents 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 or initial value in a real-world context.

Front

How do you interpret the slope in a linear equation?

Back

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

Front

What is the equation for the total cost of a service with a fixed fee and a variable cost?

Back

The equation is y = mx + b, where y is the total cost, m is the variable cost per unit, x is the number of units, and b is the fixed fee.

Front

If a T-shirt design company charges $25 plus $8 per shirt, what is the equation for the total cost?

Back

y = 8x + 25, where y is the total cost and x is the number of shirts.

Front

How do you find the number of hours for which two services cost the same?

Back

Set the equations for both services equal to each other and solve for the variable representing time.

Front

What is the equation for a holiday meal cost with a delivery fee?

Back

y = 12.50x + 30, where y is the total cost, x is the number of people, and 30 is the delivery fee.

Front

What does it mean if two linear equations intersect on a graph?

Back

The intersection point represents the values of x and y where both equations are equal, indicating the same outcome for both scenarios.

Front

How do you interpret a fixed fee in a linear equation?

Back

The fixed fee is the initial cost that does not change regardless of the number of units purchased or used.

Front

What is the significance of the variable cost in a linear equation?

Back

The variable cost represents the additional cost incurred for each unit of service or product consumed.