A straight line with equation $2y = kx + h$ passes through the points (-2, 6) and (1, -9). Find the values of $k$ and $h$. Answer k = ... , h = ...

1. Substitute the two points into the line equation to form simultaneous equations.

For $(-2,6)$:
$2(6)=k(-2)+h$
$12=-2k+h \quad \text{--- (1)}$

For $(1,-9)$:
$2(-9)=k(1)+h$
$-18=k+h \quad \text{--- (2)}$

2. Solve the simultaneous equations for $k$.

From (1),
$h=12+2k$

Substitute into (2):
$-18=k+(12+2k)$
$-30=3k$
$k=-10$

3. Find $h$ using the value of $k$.

Substitute $k=-10$ into (2):
$-18=-10+h$
$h=-8?$

Correcting the arithmetic:
$h=-18+10=-8$