Find the slopes of the lines passing through the given pointsA (2, 3) , B (4, 7)

Explanation:-

The problem provides us with two points in a 2-dimensional space, namely point A and point B. The coordinates of point A are (2, 3), which means that it is located 2 units to the right of the y-axis and 3 units above the x-axis. Similarly, the coordinates of point B are (4, 7), which means that it is located 4 units to the right of the y-axis and 7 units above the x-axis.

The problem asks us to find the slope of the line passing through points A and B. The slope of a line is defined as the change in y divided by the change in x between any two points on the line. Mathematically, this can be expressed as:

[slope = \frac{y_2 – y_1}{x_2 – x_1}]

Here, (x1, y1) and (x2, y2) are any two points on the line. We can use the coordinates of points A and B to find the slope of the line passing through them as follows:

[slope = \frac{7 – 3}{4 – 2}]

Here, we have substituted the coordinates of A and B into the slope formula. Simplifying the expression, we get:

[slope = \frac{4}{2}]

This tells us that the slope of the line passing through points A and B is 2.