Interpreting Slope and Y-intercept

Front

What does the slope of a linear equation represent?

Back

The slope represents the rate of change of the dependent variable with respect to the independent variable.

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

How do you interpret the y-intercept in a real-world context?

Back

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

Front

If a line has a negative slope, what does that indicate about the relationship between the variables?

Back

A negative slope indicates that as the independent variable increases, the dependent variable decreases.

Front

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

Back

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

Front

If a climber's altitude increases from 400 feet to 700 feet over 4 hours, what is the average rate of change?

Back

Average rate of change = (700 - 400) / (6 - 2) = 75 feet per hour.

Front

In the equation y = -10x + 500, what does the slope of -10 indicate?

Back

It indicates that James sells 10 fewer cards each day.

Front

What does a y-intercept of 500 in the equation y = -10x + 500 signify?

Back

It signifies that James starts with 500 cards to sell.

Front

How can you determine the slope from a graph?

Back

The slope can be determined by selecting two points on the line and calculating the rise over run.