Slope from a Graph and Two Points

Front

What is the definition of slope in a graph?

Back

The slope of a line is a measure of its steepness, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

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

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 is positive, what does that indicate about the line?

Back

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

Front

If the slope is negative, what does that indicate about the line?

Back

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

Front

Find the slope of the line that passes through the points (3, 4) and (7, 10).

Back

The slope is m = (10 - 4) / (7 - 3) = 6 / 4 = 3/2.

Front

Find the slope of the line that passes through the points (1, 2) and (4, 5).

Back

The slope is m = (5 - 2) / (4 - 1) = 3 / 3 = 1.

Front

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

Back

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

Front

What does a slope of 1 mean in a graph?

Back

A slope of 1 means that for every unit increase in x, y increases by the same amount, resulting in a 45-degree angle with the x-axis.