Slope from Two Points

Front

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

Back

The slope (m) is calculated using the formula: m = \frac{y2 - y1}{x2 - x1}.

Front

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

Back

Using the formula, m = \frac{7 - 3}{4 - 2} = \frac{4}{2} = 2.

Front

What does a positive slope indicate about the relationship between two variables?

Back

A positive slope indicates that as one variable increases, the other variable also increases.

Front

What does a negative slope indicate about the relationship between two variables?

Back

A negative slope indicates that as one variable increases, the other variable decreases.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

If the slope of a line is \frac{3}{4}, what does this mean in terms of rise over run?

Back

It means that for every 4 units you move horizontally (run), the line rises 3 units (rise).

Front

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

Back

Two lines are parallel if they have the same slope.

Front

How do 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 \frac{5}{2}, what is the slope of a line that is perpendicular to it?

Back

The slope of the perpendicular line would be -\frac{2}{5}.