Let y = [tex] \frac{x}{2} [/tex] + 3 be line₁
And the perpendicular angle be line₂
If a line is perpendicular to another, then the product of their gradients is -1, which means that the gradient of line₂ would be the negative reciprocal of line₁
Based on that, if the gradient of line₁ is [tex] \frac{1}{2} [/tex]
then, the gradient of line₂ is - 2.
Now by using the point-slope form y - y₁ = m ( x - x₁)
If line₂ passes through the line (1,8) and have gradient -2,
then by exploiting the point-slope form y - 8 = -2 (x - 1)
∴ equation of the ine perpendicular to y = [tex] \frac{x}{2} [/tex] + 3 would be y = -2x + 10
