Slope on 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 to the horizontal change between two points on the line.

Front

How is slope calculated using two points (x1, y1) and (x2, y2)?

Back

Slope (m) is calculated using the formula: 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 zero, 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 zero, leading to division by zero.

Front

How can you identify the slope from a graph visually?

Back

You can identify the slope by selecting two points on the line, measuring the vertical and horizontal distances between them, and calculating the ratio of these distances.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept represents the point where the line crosses the y-axis, indicating the value of y when x is zero.

Front

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

Back

A slope of 1/2 means that for every 2 units you move horizontally (run), the line rises 1 unit (rise).