The point of intersection is a point where the variables y and x will be the same in both A and B equations. This is because the point of intersection has the same coordinates for both lines. So Y_A = Y_B and so x + 4 = 0.5x + 3.5.

Given that x + 4 = 0.5x + 3.5: subtract 0.5x from both sides of the equation, x + 4 - 0.5x = 0.5x + 3.5 - 0.5x.

New equation: 0.5x + 4 = 3.5, We now have the x variable on one side only, making the equation easier to solve.

Now manipulate the equation in a way to get the variables and non-variables on opposing sides (subtract 4): 0.5x + 4 - 4 = 3.5 - 4.

New equation: 0.5x = -0.5

Final step to solve for x: Because x is being multiplied by 1/2 on the LHS and we need x to be multiplied by 1 to get it on its own, we need to multiply the LHS by 2: 0.5x * 2 = -0.5 * 2

New equation: x = -1.

Now we know what x equals, we can substitute the -1 back into the original line equations (choose A or B) to find y.

into A: y = (-1) + 4 so y = 3.

To finish, we have found x and y and so have found the point at which the two lines intersect.

X = -1, Y = 3 OR (-1,3)

Factorise fully: 3x - 9x^2

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