Independent - Slope from a graph

Front

What is the definition of slope in a graph?

Back

The slope of a line is a measure of its steepness, typically represented 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

The slope (m) can be 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-value increases, the y-value also increases, 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-value increases, the y-value decreases, 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-value changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as it represents a division by zero in the slope formula.

Front

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

Back

A slope of 2 means that for every 1 unit of horizontal change (run), the vertical change (rise) is 2 units.

Front

How can you determine the slope from a graph visually?

Back

To determine the slope visually, select two points on the line, count the vertical rise and horizontal run between them, and calculate the slope using the rise/run ratio.

Front

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

Back

The slope of the line is 3, which indicates that for every 1 unit increase in x, y increases by 3 units.

Front

What is the slope of the line represented by the equation y = -1/2x + 4?

Back

The slope of the line is -1/2, indicating that for every 1 unit increase in x, y decreases by 0.5 units.