Slope Intercept Word Problems

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept represents the value of y when x is 0, often interpreted as the starting value in a real-world context.

Front

In the equation y = mx + b, what does 'm' represent?

Back

The slope of the line, which indicates the rate of change of y with respect to x.

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What is the significance of the slope in a real-world context?

Back

The slope indicates how much y changes for a unit change in x, representing rates such as speed, cost per item, etc.

Front

What does the equation y = 1.5x + 20 represent in a word problem context?

Back

It models a situation where there is a fixed cost (20) plus a variable cost (1.5 per ride) for a total cost.

Front

How can you interpret the y-intercept in a cost function?

Back

The y-intercept represents any fixed costs that are incurred regardless of the variable costs.

Front

What is a real-world example of a linear equation?

Back

A linear equation can represent a budget where total expenses are a function of fixed costs and variable costs.

Front

How do you find the total cost if you know the number of items purchased and the cost per item?

Back

Total Cost = Fixed Cost + (Cost per Item * Number of Items).

Front

What does it mean if the slope of a line is negative?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship.

Front

How can you determine the number of customers served after a certain time using a linear equation?

Back

By substituting the time into the equation that models customers served as a function of time.