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.

Tags

CCSS.8.EE.B.5

Front

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

Back

Slope (m) = (y2 - y1) / (x2 - x1)

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.8.EE.B.5

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).

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.8.EE.B.5

Front

If a line has a slope of 1/2, what does this mean in terms of rise and run?

Back

For every 2 units you move horizontally (run), the line rises 1 unit (rise).

Tags

CCSS.8.EE.B.5

Front

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

Back

The slope of the line is 3, which is the coefficient of x in the equation.

Tags

CCSS.8.EE.B.5

Front

How can you determine the slope from a graph visually?

Back

To determine the slope visually, select two points on the line, count the vertical rise and horizontal run between them, and calculate the slope as rise/run.

Tags

CCSS.8.EE.B.5

Front

What is the slope of the line that passes through the points (1, 2) and (3, 6)?

Back

Slope = (6 - 2) / (3 - 1) = 4 / 2 = 2.

Tags

CCSS.8.EE.B.5