Answer: [tex]y = -2x - 3[/tex]
Step-by-step explanation:
Two lines are said to be perpendicular if the product of their slope = -1
Given :
[tex]4y = 2x + 5[/tex]
to find the slope , we will write it in the form : [tex]y = mx + x[/tex]
That is
[tex]y = \frac{2}{4}x + \frac{5}{4}[/tex]
[tex]y = \frac{1}{2}x + \frac{5}{4}[/tex]
which means that the slope = [tex]\frac{1}{2}[/tex]
any line that is perpendicular to this line will have slope = -2
using the formula :
[tex]y - y_{1} = m (x-x_{1})[/tex] , we have
[tex]y - (-1) = -2 ( x -(-1) )[/tex]
[tex]y + 1 = - 2 ( x + 1 )[/tex]
[tex]y + 1 = -2x - 2[/tex]
[tex]y = -2x - 2 - 1[/tex]
[tex]y = -2x - 3[/tex]
