Question

Explain how to find the equation of the line that is

perpendicular to the given line and passes through the point,
(-2,2).
(-22)
2-
to 5 3 2 1
4 5 6 x
2
(0, -3)

Answer 1

Answer: g(x) = -5*x + 12

Explanation:

If we have a linear equation f(x) = y = a*x + b

where a is the slope and b is the y-intercept.

The perpendicular line to f(x), can be written as:

g(x) = y = (-1/a)*x + c

Now, we start with a function that goes through the poins:

(-5, - 4) and (0, - 3)

We can find the slope of this function as:

a = (y2 - y1)/(x2 - x1) = (-3 -(-4))/(0 -(-5)) = 1/5

so this function is:

f(x) = y = (1/5)*x + b

now that we have the slope, we can find the perpendicular line:

g(x) = -5*x + c

now, we know that this line goes through the point (2, 2) so when x = 2, y = 2.

g(2) = 2 = -5*2 + c = -10 + c

c = 10 + 2 = 12

The function is:

g(x) = -5*x + 12