Slopes of Lines Given Two Points

Front

What is the formula to calculate the slope of a line given two points (x1, y1) and (x2, y2)?

Back

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

Front

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

Back

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

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that the line rises as it moves from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that the line falls as it moves from left to right.

Front

If the slope of a line is zero, what does this mean about the line?

Back

A slope of zero means the line is horizontal.

Front

If the slope is undefined, what does this indicate about the line?

Back

An undefined slope indicates that the line is vertical.

Front

Calculate the slope of the line that passes through the points (1, 2) and (3, 6).

Back

The slope is \frac{6 - 2}{3 - 1} = \frac{4}{2} = 2.

Front

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

Back

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

Front

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

Back

The slope is \frac{5 - 0}{5 - 0} = \frac{5}{5} = 1.

Front

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

Back

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