4-5: Interpret y-intercept and slope

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

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

Back

The y-intercept, which is the value of y when x is 0. It represents the initial value of the dependent variable.

Front

What is the meaning of a positive slope in a linear equation?

Back

A positive slope indicates that as the independent variable (x) increases, the dependent variable (y) also increases.

Front

What does a negative slope indicate in a linear equation?

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases.

Front

If the slope of a line is 0, what does that mean?

Back

A slope of 0 means that the line is horizontal, indicating that the dependent variable (y) does not change as the independent variable (x) changes.

Front

In the context of a cost equation, what does the y-intercept represent?

Back

The y-intercept represents the fixed costs or initial costs incurred before any variable costs are added.

Front

How do you interpret the slope in a cost equation like y = 12x + 200?

Back

The slope (12) indicates that for each additional person attending the party, the total cost increases by $12.

Front

What does the y-intercept of 200 mean in the equation y = 12x + 200?

Back

The y-intercept (200) means that there is an initial cost of $200, regardless of the number of people attending.

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

In the equation y = 10x + 50, what does the slope of 10 represent?

Back

The slope of 10 means that for each month (x) that Jamil stays at the fitness club, his total cost (y) increases by $10.