Slope from Two Points

Front

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

Back

The formula for the slope (m) is m = (y2 - y1) / (x2 - x1).

Front

If the coordinates of two points are (2, 3) and (4, 7), what is the slope?

Back

Using the formula m = (y2 - y1) / (x2 - x1), the slope is m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

What does a positive slope indicate about the relationship between two points on a graph?

Back

A positive slope indicates that as the x-coordinate increases, the y-coordinate also increases, showing a direct relationship.

Front

What does a negative slope indicate about the relationship between two points on a graph?

Back

A negative slope indicates that as the x-coordinate increases, the y-coordinate decreases, showing an inverse relationship.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x (denominator) is zero.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0 because there is no change in y (numerator) as x changes.

Front

How can you determine if two lines are parallel using their slopes?

Back

Two lines are parallel if they have the same slope.

Front

How can you determine if two lines are perpendicular using their slopes?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

If the slope of a line is 3, what does this mean in terms of rise over run?

Back

A slope of 3 means that for every 1 unit you move to the right (run), you move up 3 units (rise).

Front

What is the slope of the line that passes through the points (1, 2) and (1, 5)?

Back

The slope is undefined because the x-coordinates are the same, indicating a vertical line.