Slope from Two Points

Front

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

Back

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

Front

What does it mean if the slope of a line is undefined?

Back

An undefined slope indicates a vertical line, where the change in x (denominator) is zero.

Front

How do you determine if a slope is positive, negative, or zero?

Back

A positive slope rises from left to right, a negative slope falls from left to right, and a zero slope is horizontal.

Front

What is the slope of a line that passes through the points (2, 3) and (2, 5)?

Back

The slope is undefined because the x-coordinates are the same.

Front

If the slope of a line is 0, what can you say about the line?

Back

The line is horizontal.

Front

What is the slope of a line that passes through the points (1, 2) and (4, 2)?

Back

The slope is 0 because the y-coordinates are the same.

Front

How do you find the slope of a line given its equation in slope-intercept form (y = mx + b)?

Back

The slope (m) is the coefficient of x in the equation.

Front

What is the slope of a line that passes through the points (-1, -1) and (3, 3)?

Back

The slope is 1, calculated as (3 - (-1)) / (3 - (-1)) = 4/4 = 1.

Front

What is the significance of the slope in real-world applications?

Back

The slope represents the rate of change, such as speed, cost per item, or growth rate.

Front

How can you determine the slope from a graph of a line?

Back

Select two points on the line, calculate the rise (change in y) and run (change in x), then use m = rise/run.