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 a situation with a flat fee and a variable cost?

Back

The equation is typically in the form y = mx + b, where b is the flat fee and m is the variable cost per unit.

Front

If a taxi charges a flat fee plus a per-mile rate, how would you write the equation?

Back

The equation would be y = mx + b, where m is the per-mile rate and b is the flat fee.

Front

How do you find the break-even point in a word problem involving two linear equations?

Back

Set the two equations equal to each other and solve for x to find the point where both costs are the same.

Front

What is the significance of the initial fee in a linear equation word problem?

Back

The initial fee represents the starting cost before any additional charges are applied.

Front

How can you represent a situation where someone saves a fixed amount each month?

Back

You can represent it with the equation y = mx + b, where m is the amount saved per month and b is the initial amount.

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 a common solution.

Front

How do you write an equation for a service that charges per hour?

Back

The equation would be y = mx + b, where m is the hourly rate and b is any initial fee.