Slope from Graphs

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.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as there is no horizontal change.

Front

If a line has a slope of 2, what does this mean?

Back

A slope of 2 means that for every 1 unit increase in the x-direction, the y-value increases by 2 units.

Front

Find the slope of the line passing through the points (1, 2) and (4, 8).

Back

Slope = (8 - 2) / (4 - 1) = 6 / 3 = 2.

Front

Find the slope of the line passing through the points (3, 5) and (3, 1).

Back

Slope is undefined because the x-values are the same, indicating a vertical line.

Front

What is the slope of the line represented by the equation y = 3x + 1?

Back

The slope is 3, which means for every 1 unit increase in x, y increases by 3 units.