Question

A line has gradient 5.
M and N are two points on this line.
M is the point (x, 8) and N is the point (k, 23).
Find an expression for x in terms of k.

Answer 1

Rule: If m be the gradient of any straight line, then its equation can be written as

y = mx + c

Now we try to solve your problem:

Given, m = 5

Then the equation of the straight line can be

Y = 5X + C ..... (i), where C is constant

Since M (x, 8) and N (k, 23) are lying on (i) no. line, we get

8 = 5x + C ..... (ii)

23 = 5k + C ..... (iii)

• From (ii): C = 8 - 5x
• From (iii): C = 23 - 5k

Equating C, we get

8 - 5x = 23 - 5k

or, 5x = 5k + 8 - 23

or, 5x = 5k - 15

or, x = k - 3

This is the required expression for x in terms of k.

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