Linear expressions are something which contains x, y and a constant, and can therefore be plotted as a straight line, hence the word linear. This does not include squares, cubes, square roots and so on for variables x or y. The constant, however, can equal to zero.

y = 2x + 1 is linear.
3y = -2x is linear.
3y = -x + 4 is linear.
-2v = -3t - 5 is linear.
y = -2 is linear, even though it does not contain x.
x = 3 is linear, even though it does not contain y.
2y2 = x + 3 is NOT linear, since y^2 is present.
y = -2x2 + x + 1 is NOT linear, since x^2 is present.
x = 2y + 4 is linear.
2t = -u + 5 is linear.

All the said linear equations contain either one or two variables, all of which are raised to power 1. No squares, cubes etc are allowed.

For exercise 3, you first need to be able to read coordinates. We then trace the value of x given the value of y or trace the value of y given the value of x.

For exercise 4, here is how it's done.

y = 12 - 3x

The point (a, 0) is on this line. This means that when x = a, y = 0. We proceed to substitute these values into the equation y = 12 - 3x.

0 = 12 - 3a
Bringing over the -3a to the other side,
3a = 12
Dividing both sides by 3,
a = 4

The point (1, b) is on the same line. This means that when x = 1, y = b. We proceed to substitute these values into the equation y = 12 - 3x.

b = 12 - 3 (1)
b = 12 - 3 x 1
b = 12 - 3
b = 9

The point (c, 5) is also on the same line. This means that when x = c, y = 5. We proceed to substitute these values into the equation y = 12 - 3x.

5 = 12 - 3c
Bringing over -3c to the other side,
3c + 5 = 12
Bringing over 5 to the other side,
3c = 7
Dividing both sides by 3,
c = 7/3 = 2 1/3.

For exercise 5, it is done this way.

y = 20t + 30

This is a linear equation (and therefore produces a linear graph), since y is power 1 and t is power 1.

Now we look at the point A (1, 50).

Does this satisfy the above equation?

Let t = 1, y = 50.

Left hand side of the equation y = 50.
Right hand side of the equation 20t + 30 = 20 (1) + 30 = 20 x 1 + 30 = 20 + 30 = 50

Both sides are the same.

Therefore, the coordinate A satisfies the above equation, and will therefore be on the straight line when drawn on a graph.

Instead, things like (0, 5) will not satisfy the above equation, because 20 (0) + 30 = 20 x 0 + 30 = 0 + 30 = 30 which is not the same value at 5, and therefore (0, 5) will not be on the straight line when drawn on a graph.