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 do you find the slope from the equation of a line in slope-intercept form (y = mx + b)?

Back

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

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 slope from two points (x1, y1) and (x2, y2)?

Back

The slope can be calculated using the formula: slope = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, 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-value increases, the y-value decreases, resulting in a downward slant from left to right.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no vertical change as the x-value changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as there is no horizontal change.

Front

How do you convert the standard form of a linear equation (Ax + By = C) to slope-intercept form (y = mx + b)?

Back

To convert to slope-intercept form, solve for y: y = (-A/B)x + (C/B). Here, -A/B is the slope and C/B is the y-intercept.

Front

What is the significance of the y-intercept in real-world applications?

Back

The y-intercept often represents the initial value or starting point in real-world scenarios, such as costs, populations, or measurements.