32 Factorize: 3p2 + 16 33 A straight line AB passes through points A(3,2) and B(5,6). Calculate the gradient of the line. 34 A straight line whose gradient is rac13 passes through points R(8,4) and P(

Let $(x_1, y_1) = (3,2)$ and $(x_2, y_2) = (5,6)$.

The gradient $m$ is given by the formula:

The gradient of the line is $\boxed{2}$.

34 A straight line whose gradient is $\frac{1}{3}$ passes through points R(8,4) and P(5,k). Find the value of k.

Given gradient $m = \frac{1}{3}$.
Let $(x_1, y_1) = (8,4)$ and $(x_2, y_2) = (5,k)$.

Multiply both sides by $-3$:

Add 4 to both sides:

The value of $k$ is $\boxed{3}$.

35 The height of a flag post must be 8m or more but shorter than 12m. The flag post at Umoja Junior School is 2m tall. Form an inequality to represent the information.

Let $h$ be the height of the flag post in meters.
"8m or more" means $h \ge 8$.
"shorter than 12m" means $h < 12$.

Combining these two conditions, the inequality is:

36 The equation of a straight line is given as: $2x + 3y = 9$. Determine the gradient of the straight line.

Subtract $2x$ from both sides:

Divide all terms by 3:

In the form $y = mx + c$, $m$ is the gradient.
The gradient of the straight line is $\boxed*{-\frac{2}{3}}*$.

37 A straight line passes through points N(0,2) and M(8,5). Determine its equation in the form $y = mx + c$.

Let $(x_1, y_1) = (0,2)$ and $(x_2, y_2) = (8,5)$.

Since point N is $(0,2)$, this means that when $x=0$, $y=2$. In the equation $y = mx + c$, when $x=0$, $y=c$. Therefore, $c=2$.

Substitute the gradient $m = \frac{3}{8}$ and the y-intercept $c = 2$ into the form $y = mx + c$.

The equation of the line is $\boxed*{y = \frac{3}{8}x + 2}*$.