Slope (graphs, tables, points)

Front

What is 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 a graph.

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

Slope (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 does a zero slope indicate?

Back

A zero slope indicates a horizontal line where there is no change in the y-value as the x-value changes.

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line where the x-value does not change, leading to a division by zero in the slope formula.

Front

If the slope of a line is 3, what does this mean in terms of rise and run?

Back

A slope of 3 means that for every 1 unit you move horizontally (run), the line rises 3 units vertically (rise).

Front

Given the points (2, -7) and (-1, 6), what is the slope?

Back

The slope is -13/3.

Front

What is the slope of the line represented by the table of values?

Back

The slope of the line represented by the table is the change in y divided by the change in x, which can be calculated from the values.

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the same as the slope, representing how much the output (y) changes for a given change in the input (x).