which is steeper, a line with a slope of 7 or a line with a slope of -10? Can you explain it to me also?

The slope of a line in the plane containing the x and y axes is generally represented by the letter m, and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.

Thus, even though it is decreasing, the greater change is the -10.

To determine which line is steeper, we need to understand that the slope represents the rate of change in the vertical direction (y-axis) for every unit change in the horizontal direction (x-axis).

A positive slope indicates that the line is increasing as we move from left to right, while a negative slope indicates a decreasing line.

In this case, a line with a slope of 7 is steeper than a line with a slope of -10. This is because a positive slope of 7 means that for every 1 unit increase in the x-axis, the line increases by 7 units on the y-axis. In contrast, a negative slope of -10 means that for every 1 unit increase in the x-axis, the line decreases by 10 units on the y-axis.

Therefore, the line with a slope of 7 has a greater rate of change and is steeper than the line with a slope of -10.

To determine which line is steeper between a slope of 7 and a slope of -10, you need to understand the concept of slope.

In geometry, slope is a measure of the steepness of a line. It describes how much a line rises or falls as it moves horizontally. In general, higher slope values indicate a steeper line.

The slope of a line is usually represented by the letter "m". It can be positive, negative, or zero. A positive slope means the line rises from left to right, a negative slope means the line falls from left to right, and a zero slope means the line is perfectly horizontal.

Now, comparing the slopes mentioned in your question, a slope of 7 is positive, and a slope of -10 is negative. Since the absolute value of -10 is larger than 7, it means that the negative slope of -10 is steeper than the positive slope of 7.

To visualize this, imagine drawing both lines on a graph. The line with a slope of 7 would go upward from left to right but at a less steep angle compared to the line with a slope of -10, which would go downward from left to right at a steeper angle.

In summary, the line with a slope of -10 is steeper than the line with a slope of 7 because -10 has a larger absolute value than 7.