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