Let the function be defined by f(x) = 2x+1. Complete the table below.

The distance $D$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

$A = (1,3) \implies x_1 = 1, y_1 = 3$
$B = (4,7) \implies x_2 = 4, y_2 = 7$

The length of the line joining points A and B is 5 units.
The final answer is $\boxed{5}$.

4) A function is given by $y = -2x+3$, plot and find the gradient of $|AC|$ and $|BE|$.

• For A ($x = -2$): $y = -2(-2) + 3 = 4 + 3 = 7$. So $A=(-2, 7)$.
• For B ($x = -1$): $y = -2(-1) + 3 = 2 + 3 = 5$. So $B=(-1, 5)$.
• For C ($x = 0$): $y = -2(0) + 3 = 0 + 3 = 3$. So $C=(0, 3)$.
• For D ($x = 1$): $y = -2(1) + 3 = -2 + 3 = 1$. So $D=(1, 1)$.
• For E ($x = 2$): $y = -2(2) + 3 = -4 + 3 = -1$. So $E=(2, -1)$.

The completed table is:

To plot the function $y = -2x+3$, you would plot the points calculated above: $(-2, 7)$, $(-1, 5)$, $(0, 3)$, $(1, 1)$, and $(2, -1)$ on a Cartesian plane. Since this is a linear function, connecting these points will form a straight line.

The gradient $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is $m = \frac{y_2 - y_1}{x_2 - x_1}$.
For points $A=(-2, 7)$ and $C=(0, 3)$:

The gradient of $|AC|$ is $\boxed{-2}$.

For points $B=(-1, 5)$ and $E=(2, -1)$:

The gradient of $|BE|$ is $\boxed{-2}$.

5) There are how quadrants and Coordinates on the Cartesian Plane.

There are 4 quadrants on the Cartesian plane.
Coordinates are a set of values (typically an ordered pair $(x,y)$) that specify the exact location of a point on the Cartesian plane.