Finding the slope from two points

Front

What is the formula to calculate the slope between two points?

Back

The slope (m) between two points (x1, y1) and (x2, y2) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

How do you identify the coordinates of two points from a graph?

Back

To identify the coordinates of two points from a graph, locate the points on the Cartesian plane and read their x (horizontal) and y (vertical) values. Each point is represented as (x, y).

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-values increase, the y-values also increase, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, 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 change in the y-values regardless of the change in x-values.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the change in x-values is 0, leading to division by zero in the slope formula.

Front

How can you determine the slope from a set of coordinates?

Back

To determine the slope from a set of coordinates, use the slope formula: m = (y2 - y1) / (x2 - x1) by substituting the coordinates into the formula.

Front

What is the significance of the slope in real-world applications?

Back

The slope represents the rate of change between two variables, which can be applied in various fields such as physics, economics, and engineering to analyze trends.

Front

If the slope is 1, what does that tell you about the relationship between the two variables?

Back

If the slope is 1, it indicates a direct proportional relationship, meaning for every unit increase in x, there is a corresponding unit increase in y.

Front

How do you interpret a slope of -2?

Back

A slope of -2 indicates that for every 1 unit increase in x, the y-value decreases by 2 units, showing an inverse relationship.