Slope from a Graph

Front

What is the definition of slope?

Back

Slope is a measure of the steepness or incline of a line, typically represented as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

How is slope calculated from two points (x1, y1) and (x2, y2)?

Back

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

Front

What does a positive slope indicate about a line?

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?

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, indicating no vertical change as the x-values change.

Front

What is the slope of a vertical line?

Back

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

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 x, the y-value increases by 2 units.

Front

What is the slope of the line represented by the equation y = -3x + 4?

Back

The slope of the line is -3.

Front

How can you identify the slope from a graph?

Back

To identify the slope from a graph, select two points on the line, calculate the rise (change in y) and run (change in x), and then use the formula slope = rise/run.

Front

What is the slope of the line represented by the equation y = rac{1}{2}x + 1?

Back

The slope of the line is \( \frac{1}{2} \).