Answer:
[tex]y = -\frac{1}{2} x + 3[/tex]
Step-by-step explanation:
Perpendicular lines have a negative reciprocal gradient to the original line. This means you have to make the gradient negative and flip the original fraction.
The original gradient is 2 (which can be written 2/1), so the reciprocal is 1/2 and made negative it is -1/2.
Put this into the equation using form y = mx +c to get y = -1/2x + c.
To work out c, substitute the values of x and y given in the point:
5 = -1/2(-4) + c
5 = 2 + c
c = 3
Therefore, the equation for the perpendicular is:
[tex]y = -\frac{1}{2} x + 3[/tex]
