Slope and Y-Intercept

Front

What is the definition of slope in a linear equation?

Back

The slope is a measure of the steepness of a line, represented as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

How is the slope represented in the slope-intercept form of a linear equation?

Back

In the slope-intercept form, y = mx + b, 'm' represents the slope of the line.

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, resulting in an upward slant 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, resulting in a downward slant from left to right.

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where the x-values remain constant while the y-values change.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating that the y-values remain constant as the x-values change.

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of 'b' in the slope-intercept form y = mx + b.

Front

How can you determine the y-intercept from a linear equation in standard form?

Back

To find the y-intercept from the standard form Ax + By = C, set x = 0 and solve for y.

Front

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

Back

The slope can represent rates of change, such as speed, growth, or decline, in various real-world contexts.