Answer:
k = 1
Step-by-step explanation:
(i) y = kx + 10
using y = mx + c
[tex]m_{1}[/tex] = k and c= 10
(ii) 8y = (k + 7) x + 3
using y = mx + c
[tex]\frac{8y}{8} = x \frac{(k+7)} {8} + \frac{3}{8}[/tex]
such that [tex]m_{2}[/tex]= [tex]\frac{k + 7}{8}[/tex] and c = [tex]\frac{3}{8}[/tex]
using [tex]m_{1}[/tex] = [tex]m_{2}[/tex]
k = [tex]\frac{(x+7)}{8}[/tex]
8k = k + 7
8k - k = 7
[tex]\frac{7k}{7}[/tex] = [tex]\frac{7}{7}[/tex]
∴ k = 1
