Thinking with Mathematical Models - Slope & Linearity

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, 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 between two points (x1, y1) and (x2, y2)?

Back

The 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-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 the line containing the points (8,10) and (4,3)?

Back

The slope is calculated as (3 - 10) / (4 - 8) = -7 / -4 = 7/4.

Front

What is the slope of the line containing the points (1,1) and (-1,-4)?

Back

The slope is calculated as (-4 - 1) / (-1 - 1) = -5 / -2 = 5/2.

Front

What is the meaning of 'rise' in the context of slope?

Back

'Rise' refers to the vertical change between two points on a line.

Front

What is the meaning of 'run' in the context of slope?

Back

'Run' refers to the horizontal change between two points on a line.

Front

If a line has a slope of 0, what does that mean?

Back

A slope of 0 means the line is horizontal and there is no vertical change as the x-value changes.

Front

If a line has an undefined slope, what does that mean?

Back

An undefined slope means the line is vertical, and there is no horizontal change as the x-value remains constant.