Finding the Slope of Line AB with Points A(4,5) and B(9,7)

Finding the slope of a line is one of the fundamental skills you will learn in your math class. Slope refers to the degree of steepness of a line, and it is represented by the letter ‘m.’ Because of its importance in graphing coordinates and equations, it is essential that you know how to calculate the slope of a line. In this article, we will look at a concrete example to help you understand how to find the slope of a line. Specifically, we will look at finding the slope of Line AB with Points A(4,5) and B(9,7).

Before we dive into the details of finding the slope of Line AB, let us first define what a slope is. As we have mentioned, the slope of a line represents its degree of steepness. It tells us how much a line rises or falls as we move from left to right along the x-axis. In other words, it tells us how much the y-value will increase (or decrease) if we increase (or decrease) the x-value by one unit.

To calculate the slope of Line AB, we use the formula:

m = (y2 – y1) / (x2 – x1)

Where:
• m is the slope of the line
• (x1,y1) and (x2,y2) are the coordinates of two points on the line

Looking at our problem, we see that we are given the coordinates of two points: A(4,5) and B(9,7). Using these coordinates, we can substitute the values into the formula and solve for the slope.

m = (7 – 5) / (9 – 4)
m = 2 / 5
m = 0.4

We have now calculated the slope of Line AB. The slope of the line is 0.4, which means that as we move from left to right along the x-axis, the y-value increases by 0.4 units.

It is essential to note that the slope of a line can also tell us other information about the line. For instance, if the slope of a line is positive, it means that the line is increasing (i.e., it is moving upwards) as we move from left to right along the x-axis. If the slope of a line is negative, it means that the line is decreasing (i.e., it is moving downwards) as we move from left to right along the x-axis. If the slope of a line is zero, it means that the line is horizontal (i.e., it is not moving up or down).

Furthermore, if the slope of a line is undefined, it means that the line is vertical (i.e., it is moving up or down). A vertical line has no slope, but its equation can be expressed as x = k, where k is the x-coordinate of any point on the line.

In conclusion, finding the slope of a line is a critical skill in math. It allows us to determine the steepness of a line, which can give us more information about the graphed coordinates and equations. In this article, we looked at finding the slope of Line AB with Points A(4,5) and B(9,7) as an example. We used the formula m = (y2 – y1) / (x2 – x1) and substituted the coordinates of the two points to solve for the slope, which was 0.4. With this information, we can now interpret more about this line and its behavior.

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