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, typically represented 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) 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, showing a direct relationship.

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, showing an inverse relationship.

Front

What is the slope of a vertical line?

Back

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

Front

How can you identify the slope of a line from a graph visually?

Back

You can identify the slope visually by selecting two points on the line, measuring the vertical rise and horizontal run between them, and calculating the ratio of rise to run.

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 indicates a 45-degree angle.