Finding Slope from Two Points

Front

What is the formula for calculating 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 the relationship between two points?

Back

A positive slope indicates that as the x-coordinate increases, the y-coordinate also increases, showing a direct relationship between the two variables.

Front

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

Back

A negative slope indicates that as the x-coordinate increases, the y-coordinate decreases, showing an inverse relationship between the two variables.

Front

What is the slope of a vertical line?

Back

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

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0 because there is no change in y (numerator) as x changes.

Front

How can you determine if two points lie on a line with a specific slope?

Back

To determine if two points lie on a line with a specific slope, calculate the slope using the two points and compare it to the given slope.

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 biology to analyze trends.

Front

How do you interpret a slope of 1/4 in a real-world context?

Back

A slope of 1/4 means that for every 4 units increase in the x-variable, the y-variable increases by 1 unit, indicating a gradual increase.

Front

What is the relationship between slope and linear equations?

Back

In linear equations of the form y = mx + b, 'm' represents the slope, indicating the steepness and direction of the line.