Solve the Following:

(a) What is the equation for the line the sum of whose X and Y coordinates is always 8? Find a point on this line which is at a distance of 2 units from the X axis in the positive direction?

(b) Write the equation y = 3x + 2 in the form ax + by + c = 0, and indicate the value of a b and c. [4 MARKS]

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Solution

Equations : 1 Mark each
Results : 1 Mark each

(a) X coordinate + Y coordinate = 8
The required equation will be x + y = 8
A point which is 2 units away in the positive direction from the X axis will have an ordinate 2.
Putting y = 2 in the above equation, we get x = 6
Thus, the required point is (6, 2)

(b) y = 3x + 2
Rearranging,
3x – y + 2 = 0
This is of the form ax + by + c = 0
Comparing, we can see that
a = 3
b = -1
c = 2

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