Interpreting Slope and Y-intercept

Front

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

Back

The y-intercept represents the value of y when x is 0, indicating the starting point of the relationship.

Front

What is the slope in a linear equation?

Back

The slope indicates the rate of change of y with respect to x, showing how much y increases or decreases as x increases.

Front

If a line has a slope of 3, what does this mean in context?

Back

It means that for every 1 unit increase in x, y increases by 3 units.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as x increases, y decreases.

Front

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

Back

The y-intercept represents the fixed cost or starting cost when no units are produced or consumed.

Front

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

Back

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

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.

Front

What is the significance of the slope in a real-world scenario, such as a delivery cost?

Back

The slope represents the variable cost per unit, such as the cost per additional item delivered.

Front

If a graph shows a steep slope, what does this imply?

Back

A steep slope implies a large change in y for a small change in x, indicating a strong relationship.

Front

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

Back

A negative y-intercept means that the starting value of y is below zero when x is zero.