Slope Review 3

Front

What is the definition of slope in mathematics?

Back

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 (y = mx + b). It is calculated as the change in y (rise) over the change in x (run).

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 is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no change in y regardless of the change in x.

Front

What is the slope of a vertical line?

Back

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

Front

Find the slope of the line that passes through the points (2, 3) and (4, 7).

Back

The slope is m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

Find the slope of the line that passes through the points (1, 2) and (3, -2).

Back

The slope is m = (-2 - 2) / (3 - 1) = -4 / 2 = -2.

Front

If a line has a slope of 3/4, what does this mean in terms of rise and run?

Back

For every 4 units the line moves horizontally (run), it moves up 3 units (rise).

Front

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

Back

The slope is -2, which indicates the line falls as it moves from left to right.