Slope and y Intercept from Word Problems

Front

What does the slope represent in a linear equation?

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 unit change 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 represents the starting point of the line on the y-axis.

Front

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

Back

'm' represents the slope of the line.

Front

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

Back

'b' represents the y-intercept of the line.

Front

If a coffee costs $3, how would you represent this in a linear equation for a coffee fund?

Back

y = -3x + initial amount, where x is the number of coffees bought.

Front

How do you find the number of hours rented if the total cost is known?

Back

Set the total cost equal to the equation and solve for x.

Front

What does a negative slope indicate in a real-world context?

Back

A negative slope indicates a decrease in the dependent variable as the independent variable increases.

Front

What is the significance of the y-intercept in a word problem?

Back

It often represents the starting value or initial condition before any changes occur.

Front

How can you determine the cost of renting a moped for a certain number of hours?

Back

Use the equation y = mx + b, where m is the cost per hour and b is any flat fee.

Front

What does it mean if the y-intercept is a negative number?

Back

It indicates that the initial value of the dependent variable is below zero, which may not be possible in some contexts.