The slope of the line? positive negative zero undefined

Question: The slope of the line? positive negative zero undefined

The slope of a line is a measure of how steeply it rises or falls as we move along the x-axis. The slope can be positive, negative, zero, or undefined depending on the direction and shape of the line. In this blog post, we will explore each of these cases and how to find the slope using the formula m = (y2 - y1) / (x2 - x1), where m is the slope and (x1, y1) and (x2, y2) are two points on the line.

A line has a positive slope if it goes up from left to right. This means that as we increase the value of x, the value of y also increases. For example, the line y = 2x + 5 has a positive slope of 2. To find the slope, we can pick any two points on the line and plug them into the formula. For instance, if we choose (0, 5) and (1, 7), we get m = (7 - 5) / (1 - 0) = 2 / 1 = 2.

A line has a negative slope if it goes down from left to right. This means that as we increase the value of x, the value of y decreases. For example, the line y = -3x + 2 has a negative slope of -3. To find the slope, we can use the same formula as before. For instance, if we choose (0, 2) and (1, -1), we get m = (-1 - 2) / (1 - 0) = -3 / 1 = -3.

A line has a zero slope if it is horizontal. This means that the value of y does not change as we move along the x-axis. For example, the line y = 4 has a zero slope. To find the slope, we can use any two points on the line and plug them into the formula. We will always get m = 0 / (x2 - x1) = 0 for any value of x.

A line has an undefined slope if it is vertical. This means that the value of x does not change as we move along the y-axis. For example, the line x = -2 has an undefined slope. To find the slope, we cannot use the formula because it would involve dividing by zero, which is not possible. We can say that m is undefined or does not exist for a vertical line.