First find the equation of y.
[tex]y=mx+n=\frac{\Delta y}{\Delta x}x+n[/tex]
Find the slope m.
[tex]m=\frac{5-9}{-1-3}=\frac{-4}{-4}=1[/tex].
Pick one point, I'll pick (-3, 9). Insert coordinates in equation then compute n.
[tex]9=1(-3)+n\implies n=12[/tex].
The equation of a line y is:
[tex]y=x+12[/tex].
The perpendicular line [tex]y_{\perp}[/tex] is same like the normal line except its slope m becomes:
[tex]k=-\frac{1}{m}=-1[/tex].
The equation of a perpendicular bisector is thus:
[tex]y_{\perp}=-x+12[/tex].
Hope this helps.
Answer:
[tex]y = \frac{1}{2} x + 3[/tex]
Step-by-step explanation:
Using the given points, first find the slope:
m = (₂ - y₁) / (x₂ - x₁)
= (5 - 9) / (-1 - (-3))
= -4 / 2
= -2
Find y-intercept by using anyone of the give points and slope from above:
y = mx + b
5 = -2(-1) + b
5 = 2 + b
b = 3
With the m and b, you can make equation of line:
y = mx + b
y = -2x + 3
To find the perpendicular slope, make it opposite and inverse it.
m = -2 becomes 1/2
Regular equation of line:
y = -2x + 3
Perpendicular equation of line:
[tex]y = \frac{1}{2} x + 3[/tex]
