Slope from a Graph

Front

What is the definition of slope in a graph?

Back

Slope is a measure of the steepness or incline of a line, 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 from two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1)

Front

What does a positive slope indicate about a line on a graph?

Back

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

Front

What does a negative slope indicate about a line on a graph?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, meaning the line falls from left to right.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no vertical change (rise) regardless of the horizontal change (run).

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the horizontal change (run) is 0, leading to division by zero.

Front

If a line has a slope of 3, what does this mean?

Back

A slope of 3 means that for every 1 unit increase in the x-direction, the y-value increases by 3 units.

Front

Find the slope of the line that passes through the points (2, 3) and (5, 11).

Back

Slope = (11 - 3) / (5 - 2) = 8 / 3.

Front

What is the slope of the line represented by the equation y = -2x + 4?

Back

The slope is -2, which indicates the line falls as it moves from left to right.

Front

How can you identify the slope from a graph visually?

Back

You can identify the slope by selecting two points on the line, counting the vertical rise and horizontal run between them.