Find the coordinates of the intercepts and the gradients of the lines 4x − 2y = 8 and x + y = -1, and their intersection point E.

So, point A is $(2, 0)$.

So, point B is $(0, -4)$.
The coordinates are $\boxed{\text{A}(2, 0) \text{ and B}(0, -4)}$.

b) The coordinates of C and D
Line: $x + y = -1$

So, point D is $(-1, 0)$.

So, point C is $(0, -1)$.
The coordinates are $\boxed{\text{C}(0, -1) \text{ and D}(-1, 0)}$.

c) The gradient of $4x - 2y = 8$

The gradient $m$ is the coefficient of $x$.
The gradient is $\boxed{2}$.

d) The gradient of $x + y = -1$

The gradient $m$ is the coefficient of $x$.
The gradient is $\boxed{-1}$.

e) The coordinates of E
Point E is the intersection of $4x - 2y = 8$ and $x + y = -1$.

From the second equation, $y = -x - 1$.
Substitute this into the first equation:

The coordinates of E are $\boxed{(1, -2)}$.

f) The values of x for which the lines are increasing or decreasing

For $4x - 2y = 8$, the gradient is 2 (from part c). Since $2 > 0$, this line is increasing.
For $x + y = -1$, the gradient is $-1$ (from part d). Since $-1 < 0$, this line is decreasing.
The line $4x - 2y = 8$ is increasing for all values of $x$.
The line $x + y = -1$ is decreasing for all values of $x$.
$\boxed{\text{Line } 4x - 2y = 8 \text{ is increasing for all } x. \text{ Line } x + y = -1 \text{ is decreasing for all } x.}$

2. Given: $3x - y = 4$ and $2x - y = 5$

a) On the same set of axes, draw neat sketch graphs of the two functions.
To sketch the graphs, we find two points for each line, typically the intercepts.
For $3x - y = 4$:
If $x=0$, then $-y=4 \implies y=-4$. Point: $(0, -4)$.
If $y=0$, then $3x=4 \implies x=\frac{4}{3}$. Point: $(\frac{4}{3}, 0)$.
For $2x - y = 5$:
If $x=0$, then $-y=5 \implies y=-5$. Point: $(0, -5)$.
If $y=0$, then $2x=5 \implies x=\frac{5}{2}$. Point: $(\frac{5}{2}, 0)$.
To draw the sketch, plot these points for each line and connect them. The lines will intersect at the point found in part (b).

b) Determine the coordinates of the point of intersection.
We have the system of equations:

1. $3x - y = 4$
2. $2x - y = 5$

Using equation (1):

The coordinates of the point of intersection are $\boxed{(-1, -7)}$.

3. Determine the equations of the following lines in the form $f(x) = ax + q$.
The image shows a line passing through $(-3, 0)$ and $(0, 6)$.
The form $f(x) = ax + q$ is equivalent to $y = mx + c$, where $a$ is the gradient and $q$ is the y-intercept.

The line crosses the y-axis at $(0, 6)$, so $q=6$.

The equation of the line is $\boxed{f(x) = 2x + 6}$.