Positive Slope on 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 between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula: 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 is the slope of a line that rises 4 units for every 3 units it runs?

Back

The slope of the line is 4/3.

Front

If a line has a slope of 1/2, what does this mean in terms of rise and run?

Back

For every 2 units the line runs horizontally, it rises 1 unit vertically.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the run (horizontal change) is zero.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0 because there is no vertical change (rise) as the line runs horizontally.

Front

How can you determine the slope from a linear equation in the form y = mx + b?

Back

In the equation y = mx + b, 'm' represents the slope of the line.

Front

What is the slope of a line represented by the equation y = 4x + 1?

Back

The slope of the line is 4.

Front

If a line has a slope of 2/7, what does this tell you about its steepness?

Back

A slope of 2/7 indicates a relatively gentle incline, as the rise is much smaller than the run.