Answer:
y = - (1/2) x + 1
Step-by-step explanation:
The given equation of the line is:
2 x - y - 7 = 0
solving for y gives:
2 x - 7 = y
so y = 2 x - 7
where the slope is "2", which is fundamental to know in order to construct a perpendicular line to it by using the "opposite of the reciprocal" of the given slope.
So in our case, the slope of the perpendicular line must be: "- 1 / 2" (negative one half).
now we can build the equation of the new line, using this slope and requesting the point (4, -1) to be in it:
y = - (1/2) x + b
-1 = - (1/2) (4) + b
-1 = - 2 + b
solve for b:
b = 2 - 1 = 1
Then the equation of the perpendicular line is:
y = - (1/2) x + 1
