Point A has coordinates (3,8), and point B has coordinates (x,13). The gradient of line AB is 2.5. Determine the value of x.

To determine the value of x for point B, we need to use the formula for the gradient (or slope) of a line between two points:

Gradient (slope) = (Change in y) / (Change in x) = (y2 - y1) / (x2 - x1)

From the question, we know that the gradient of line AB is 2.5. The coordinates of point A are (3,8), and the coordinates of point B are (x,13). Using these points, we can plug into the formula as follows:

2.5 = (13 - 8) / (x - 3)

We are given that: Gradient (slope) = 2.5 y2 (from point B) = 13 y1 (from point A) = 8 x2 (from point B) is what we're looking for, represented as x x1 (from point A) = 3

So, the equation becomes: 2.5 = (13 - 8) / (x - 3) 2.5 = 5 / (x - 3)

Now we need to solve for x. First, multiply both sides by (x - 3) to remove the fraction: 2.5 * (x - 3) = 5

Distribute 2.5 to both terms in the parentheses: 2.5x - 7.5 = 5

Finally, add 7.5 to both sides to solve for x: 2.5x = 5 + 7.5 2.5x = 12.5

Now divide both sides by 2.5: x = 12.5 / 2.5 x = 5

Therefore, the x-coordinate of point B is 5.