Slope of a Line

Front

What is the formula to calculate the slope of a line given 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 the direction of a line?

Back

A positive slope indicates that the line rises from left to right.

Front

What does a negative slope indicate about the direction of a line?

Back

A negative slope indicates that the line falls from left to right.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

In the equation of a line y = mx + b, what does 'b' represent?

Back

In the equation y = mx + b, 'b' represents the y-intercept of the line.

Front

How can you determine if a slope is undefined from a graph?

Back

A slope is undefined if the line is vertical, meaning it does not have a defined rise over run.

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.

Front

How do you find the slope from a linear equation in standard form Ax + By = C?

Back

To find the slope from the standard form, rearrange the equation into slope-intercept form (y = mx + b) and identify 'm'.

Front

What is the slope of the line that passes through the points (1, 2) and (3, 6)?

Back

The slope is 2, calculated as (6 - 2) / (3 - 1).