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, 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 of a line given 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 (rise) regardless of the horizontal change (run).

Front

What is the slope of a vertical line?

Back

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

Front

If a line has a slope of 4/1, what does this mean in terms of rise and run?

Back

For every 1 unit the line moves horizontally (run), it moves up 4 units (rise).

Front

If a line has a slope of -3/2, what does this mean in terms of rise and run?

Back

For every 2 units the line moves horizontally (run), it moves down 3 units (rise).

Front

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

Back

The slope of the line is 2, which is the coefficient of x in the equation.

Front

How can you determine the slope from a graph visually?

Back

You can determine the slope by selecting two points on the line, measuring the vertical change (rise) and the horizontal change (run), and calculating the ratio rise/run.