Slope

Front

What is the definition of slope?

Back

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

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 does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, meaning the line rises 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, meaning the line falls from left to right.

Front

What does a slope of zero mean?

Back

A slope of zero means that the line is horizontal, indicating that there is no change in the y-value as the x-value changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs in vertical lines, where the x-value does not change, leading to division by zero in the slope formula.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation: y = mx + b, where m is the slope and b is the y-intercept.

Front

If a car drives 360 miles in 3 hours, what is the slope representing the speed of the car?

Back

The slope (speed) is 120 miles per hour, calculated as 360 miles / 3 hours.

Front

Given the points (2, 4) and (6, 16), calculate the slope.

Back

The slope is 3, calculated as (16 - 4) / (6 - 2).

Front

What is the slope of the line represented by the equation y = 5x + 2?

Back

The slope of the line is 5.