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 of a line given 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-value increases, the y-value also increases, 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-value increases, the y-value decreases, 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 regardless of the horizontal change.

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 is 0, leading to division by zero.

Tags

CCSS.8.EE.B.5

Front

If a line has a slope of 1, what does this mean?

Back

A slope of 1 means that for every unit increase in x, there is a corresponding unit increase in y, resulting in a 45-degree angle with the x-axis.

Tags

CCSS.8.EE.B.5

Front

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

Back

The slope of the line is 2, 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?

Back

To determine the slope from a graph, select two points on the line, calculate the rise (change in y) and run (change in x), and then divide rise by 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