Question

Can someone help me please? (Math)

Answer 1

Let   y = $\frac{x}{2}$  +  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 $\frac{1}{2}$
                   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 = $\frac{x}{2}$  +  3   would  be y = -2x + 10