Question

Please solve this 4 marks question​

Answer 1

Answer:

• Yes, the point (-2, -6) lies on that same line.

• The line cuts the x-axis at (2, 0).

• The line cuts the y-axis at (0, -3).

That the point (4, 3) lies on the line means that putting x=4 and y=3 makes the equation hold true.  This enables us to work out the value of a:

 3x - ay = 6  ⇒  3×4 - a×3 = 6  ⇒  12 - 3a = 6  ⇒  3a = 6  ⇒  a = 2

So the equation of the line is

   3x - 2y = 6.

The point (-2, -6) then lies on the line if putting x = -2 and y = -6 makes the equation hold true, so put these values in to check:

  3x - 2y = 3×-2 - 2×-6  = -6 + 12 = 6    ✓

So yes, the point (-2, -6) lies on that same line, too.

For the coordinates of the point where the line cuts the x-axis, this is a point of the form (x, 0), where y=0.  So put y=0 into the equation of the line and solve for x:

  3x - 0 = 6  ⇒  x = 2  ⇒  The line cuts the x-axis at (2, 0).

Similarly, the line cuts the y-axis at a point (0, y), where x=0.  So put x=0 and solve for y:

 0 - 2y = 6  ⇒  y = -3  ⇒  The line cuts the y-axis at (0, -3).