Slope from graphs and points

Front

What is the definition of slope?

Back

The slope of a line is a measure of its steepness, usually 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 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-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?

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 an undefined slope mean?

Back

An undefined slope occurs in vertical lines where the change in x (run) is zero, making the slope calculation impossible.

Front

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

Back

The slope of the line is 2, which means for every 1 unit increase in x, y increases by 2 units.

Front

What is the slope of the line represented by the equation y = -rac{1}{2}x + 4?

Back

The slope of the line is -rac{1}{2}, indicating that for every 1 unit increase in x, y decreases by rac{1}{2} units.

Front

Given the points (1, 2) and (3, 6), what is the slope?

Back

The slope is 2, calculated as (6 - 2) / (3 - 1) = 4 / 2 = 2.

Front

What is the slope of the line that passes through the points (5, -11) and (25, 9)?

Back

The slope is 1, calculated as (9 - (-11)) / (25 - 5) = 20 / 20 = 1.

Front

Which type of line has a slope of 0?

Back

A horizontal line has a slope of 0, indicating that there is no vertical change as x changes.