Slope

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 on a graph?

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 the direction of a line on a graph?

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 vertical line?

Back

The slope of a vertical line is undefined because the change in x (denominator) is zero.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0 because the change in y (numerator) is zero.

Front

How do you determine if a slope is positive, negative, or undefined from a graph?

Back

If the line rises from left to right, the slope is positive; if it falls, the slope is negative; if it is vertical, the slope is undefined.

Front

Given the points (3, 4) and (3, 10), what is the slope of the line?

Back

The slope is undefined because the x-coordinates are the same, indicating a vertical line.

Front

If a line has a slope of -2, what does this tell you about the relationship between x and y?

Back

For every 1 unit increase in x, y decreases by 2 units.

Front

What is the slope of the line that passes through the points (0, 0) and (5, 5)?

Back

The slope is 1, indicating a 45-degree angle line that rises from left to right.

Front

How can you find the slope of a line using its equation in slope-intercept form (y = mx + b)?

Back

In the equation y = mx + b, m represents the slope of the line.