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.

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)

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.

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.

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.

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.

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 line.

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.

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.

Front

What is the slope of the line that passes through the points (2, 3) and (4, 7)?

Back

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