Slopes

Front

What is the slope?

Back

The slope is a measure of the steepness or incline of a line, typically represented as 'm' in the slope-intercept form of a linear equation.

Front

What does a positive slope indicate?

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?

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 is the slope of a horizontal line?

Back

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

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x is 0, leading to division by zero.

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

Find 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).

Front

Find the slope of the line that passes through the points (4, 5) and (4, 9).

Back

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

Front

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

Back

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

Front

What is the y-intercept in the equation y = 3x + 4?

Back

The y-intercept is 4, which is the value of y when x = 0.