Warmup 1/2

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 divided by the change in x (rise/run).

Front

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

Back

The slope (m) can be 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

Calculate the slope of the line passing through the points (2, 3) and (4, 7).

Back

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

Front

Find the slope of the line that passes through the points (10, 1) and (5, 2).

Back

The slope is (2 - 1) / (5 - 10) = 1 / -5 = -1/5.

Front

What is the slope of the line that passes through the points (-4, 7) and (-6, -4)?

Back

The slope is (-4 - 7) / (-6 + 4) = -11 / -2 = 11/2.

Front

If a line has a slope of -4/3, what does this tell you about the line's direction?

Back

The line falls from left to right, indicating that for every 4 units the line goes down, it goes 3 units to the right.