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

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 does a slope of zero indicate about a line?

Back

A slope of zero indicates a horizontal line, meaning there is no change in the y-coordinate as the x-coordinate changes.

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates a vertical line, meaning the x-coordinate does not change while the y-coordinate changes.

Front

Find the slope of the line that passes through the points (2, 3) and (4, 7).

Back

The slope is m = \frac{7 - 3}{4 - 2} = \frac{4}{2} = 2.

Front

Find the slope of the line that passes through the points (-1, -2) and (3, 2).

Back

The slope is m = \frac{2 - (-2)}{3 - (-1)} = \frac{4}{4} = 1.

Front

Find the slope of the line that passes through the points (0, 0) and (0, 5).

Back

The slope is undefined because the x-coordinates are the same (0).

Front

What is the slope of a line represented by the equation y = 3x + 2?

Back

The slope is 3, which is the coefficient of x in the equation.

Front

If a line has a slope of -2, what does this tell you about the line's direction?

Back

The line falls from left to right, indicating a negative relationship between x and y.