A is the point with coordinates (5, 9) B is the point with coordinates (d, 15) The gradient of the line AB is 3 Work out the value of d.

To work out the coordinates of point B, you need to look at all of the information that is given in the question.The question tells you that the gradient of the line is 3, which implies that we need to use the general equation of a straight line: y = mx + c, where y is the y coordinate, m is the gradient, x is the x coordinate and c is the y intercept. The first step of answering the question is substituting the coordinates of point A and the gradient into the equation of a straight line. This will give you 9 = 3(5) + c. This can be rearranged to find c:9 = 3(5) + c9 = 15 + c-6 = cThe second step is therefore substituting the coordinates of point B, the gradient and the y intercept into y = mx + c. This will give you 15 = 3d – 6. This can be rearranged to find c:15 = 3d – 6 21 = 3d7 = dThe final answer is therefore d = 7.