K is the point $(7, -8)$ and L is the point $(x, y).\n\nThe gradient of the line KL is$\frac{2}{3}$.\n\nMaverick claims that it is possible to express$x$in terms of$y$, such that$x = a + by$, where$a$and$b$ are constants.\n\nExplain why Maverick is correct.

1. Form an equation using the gradient formula for points $K(7,-8)$ and $L(x,y)$.

Gradient of $KL$:
$\frac{y-(-8)}{x-7}=\frac{2}{3}$
$\frac{y+8}{x-7}=\frac{2}{3}$

2. Rearrange the equation to express $x$ in terms of $y$ and identify the required form.

$\frac{y+8}{x-7}=\frac{2}{3}$
$3(y+8)=2(x-7)$
$3y+24=2x-14$
$2x=3y+38$
$x=\frac{3}{2}y+19$
So $x=19+\frac{3}{2}y$, which is of the form $x=a+by$.