The gradient of AB is -2, it just doesn’t show due to formatting issues.

Hi @Kieran, that is correct, the gradient of line AB is equal to -2.

**Line AB:** y = mx + c

m = (-7-9)/(10-2) = -2

In order to find *c* we can substitute the coordinates of one of the points belonging to the line into the equation:

**A (2,9):** 9 = -2*2 + c

c = 13

Final equation of the line AB: **y = -2x + 13**

Next we can find the equation of **line AC:**

As we know, lines AB and AC are perpendicular, which means their gradients are reciprocal and have opposite signs:

*NB: the reciprocal is the inverse value of a number, for example the reciprocal of number n is 1/n*. The reciprocal number of 2 is 1/2, or 0.5.

**Line AC:** y = 0.5x + c

To find the y-intercept, *c*, we can again substitute the coordinates of a point that belongs to the line AC, which is *A (2,9)*:

9 = 0.5*2 + c

c = 8

Equation of the line AC: **y = 0.5x + 8**

Lastly, we need to find the y-coordinate of point *C*. We will do that by substituting 6 for *x* in the equation of the line AC:

y = 0.5*6 + 8 = 11

**k = 11**

hi Kieran

you have correctly found the gradient of line AB = -2

We know that line AC is perpendicular to line AB therefore the gradient of line AC is -1/2

we also know that a point on line AC is (2,9)

So we can now work out what k is (6,k) by substituting x=6 into the equation

1/2 x 6 + 8 = 3 + 8 = 11

here is an image of the graph