Question

Give the equation of the line perpendicular to the line through (3, 2) and (-2, 4) that

Answer 1

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