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 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 on a graph?

Back

A positive slope indicates that as the x-values increase, the y-values also increase, resulting in an upward trend.

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, resulting in a downward trend.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no vertical change as the x-values change.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as it involves division by zero (no horizontal change).

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) where b is the y-coordinate.

Front

How can you identify the y-intercept from a graph?

Back

The y-intercept can be identified as the point where the line intersects the y-axis.

Front

If a line has a slope of -3, what does this tell you about its steepness?

Back

A slope of -3 indicates a steep downward incline, meaning for every 1 unit increase in x, y decreases by 3 units.

Front

What is the relationship between slope and the angle of inclination of a line?

Back

The slope of a line is related to the angle of inclination; a steeper line has a greater absolute value of slope.