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

The slope (m) can be calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What does a slope of 0 indicate about a line on a graph?

Back

A slope of 0 indicates that the line is horizontal, meaning there is no vertical change as you move along the line.

Front

What does a positive slope indicate about the relationship between two variables?

Back

A positive slope indicates that as one variable increases, the other variable also increases.

Front

What does a negative slope indicate about the relationship between two variables?

Back

A negative slope indicates that as one variable increases, the other variable decreases.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the run (horizontal change) is 0, leading to division by zero.

Front

How can you determine the slope of a line from its graph?

Back

To determine the slope from a graph, select two points on the line, find the rise (vertical change) and run (horizontal change) between them, and then use the slope formula.

Front

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

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x is 0.

Front

How does the slope affect the angle of a line on a graph?

Back

The greater the absolute value of the slope, the steeper the angle of the line; a slope of 1 or -1 indicates a 45-degree angle.