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.

Pls help it’s emergency!!

Answer 1

x = k - 3

Explanation:

Given parameters:

Gradient of the line = 5;

Coordinates; M(x, 8)

N(k, 23)

Solution:

If we use the expression for finding the slope of the line, we can solve this problem;

Slope =
`(y_(2) - y_(1) )/(x_(2) - x_(1) )`

where

x₁ = x y₁ = 8

x₂ = k y₂ = 23

Input the parameters:

5 =
`(23 - 8)/(k -x )`

15 = 5(k - x)

3= k- x

k - x = 3

Express x in terms of k;

-x = 3 - k

Multiply through by -1;

x = -3 + k

x = k - 3