Interpreting Slope and Y-intercept

Front

What does the slope of a linear equation represent in a real-world context?

Back

The slope represents the rate of change of one variable with respect to another, indicating how much one quantity changes for a unit change in another quantity.

Front

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

Back

In the equation y = mx + b, 'm' represents the slope of the line.

Front

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

Back

In the equation y = mx + b, 'b' represents the y-intercept, which is the value of y when x is 0.

Front

How can you interpret the slope in the context of a cost function?

Back

The slope indicates how much the total cost increases for each additional unit of the variable (e.g., each additional ride or mile driven).

Front

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

Back

A negative slope indicates that as one variable increases, the other variable decreases, showing an inverse relationship.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept represents the starting value of the dependent variable when the independent variable is zero.

Front

How do you find the slope from two points on a graph?

Back

The slope can be calculated using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What does the slope represent in the context of a moving truck rental equation?

Back

The slope represents the per-mile fee charged for renting the moving truck.

Front

In the context of a water tank releasing water, how is the slope interpreted?

Back

The slope represents the rate at which water is being released from the tank, measured in gallons per minute.

Front

What does a y-intercept of $1500 indicate in a salary equation?

Back

It indicates the base salary before any commissions or additional earnings are added.