Slope from Two Points

Front

What is the formula for calculating the slope between two points?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-coordinate increases, the y-coordinate also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-coordinate increases, the y-coordinate decreases, meaning the line falls from left to right.

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 do you find the slope from a table of values?

Back

To find the slope from a table, select two points (x1, y1) and (x2, y2) from the table and apply the slope formula: m = (y2 - y1) / (x2 - x1).

Front

If the slope of a line is 2, what does this mean in terms of rise over run?

Back

A slope of 2 means that for every 1 unit you move to the right (run), the line rises 2 units (rise).

Front

What is the slope of the line that passes through the points (3, 4) and (7, 8)?

Back

The slope is calculated as m = (8 - 4) / (7 - 3) = 4 / 4 = 1.

Front

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

Back

The slope can represent rates of change, such as speed, growth, or any relationship where one quantity changes in relation to another.

Front

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

Back

Two lines are parallel if they have the same slope.