Answer:
y=(5/2)x - 3/2
Step-by-step explanation:
We can start by finding the equation of the line given from the points. To do this, we will calculate the slope first then the y-intercept.
Line Equation: y=mx+b
Finding the slope value,
m= (y2-y1)/(x2-x1)
m=(4-2)/(-2-3)
m=-2/5
Finding the y-intercept,
y=(-2/5)x+b
Substituting one of the two coordinate pairs into the equation,
2=(-2/5)3+b
2=-6/5 +b
b=16/5
Thus the equation of the line is y=(-2/5)x + 16/5
To find the line perpendicular to this line, we have to take the negative reciprocal of the slope. So our equation for the perpendicular line is,
y=(5/2)x + b
Since the perpendicular line passes through (1,1), we can substitute this point to get the value of b,
1=(5/2)1 +b
1=5/2 + b
b= -3/2
Therefore, the equation of the line is y=(5/2)x - 3/2
