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, 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 of a line given 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 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 regardless of the horizontal change.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the horizontal change is 0, leading to 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 the line moves to the right (run), it moves down 2 units (rise).

Front

How can you determine the slope from a graph visually?

Back

To determine the slope from a graph, select two points on the line, count the vertical change (rise) and the horizontal change (run), and then use the slope formula (rise/run).

Front

What is the slope of the line represented by the equation y = 3x + 2?

Back

The slope of the line represented by the equation y = 3x + 2 is 3, which is the coefficient of x.

Front

What is the relationship between slope and parallel lines?

Back

Parallel lines have the same slope; they never intersect and maintain a constant distance apart.