November 29th Flashcardziz: Recognizing Slope on Graphs

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 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 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 does a slope of 0 mean?

Back

A slope of 0 means the line is horizontal, indicating that there is no change in the y-value as the x-value changes.

Front

What does it mean if a slope is undefined?

Back

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

Front

Given the points (2, 3) and (4, 7), what is the slope?

Back

Slope = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

If a line has a slope of -4/3, what does this tell you about its direction?

Back

The line descends from left to right, indicating a negative relationship between the x and y values.

Front

What is the slope of a line that is perfectly vertical?

Back

The slope of a vertical line is undefined.

Front

What is the slope of a line that is perfectly horizontal?

Back

The slope of a horizontal line is 0.