The value of the function f(x) is 152 when x=−5 and is −732 when x=3 . What is the equation of the function?(1 point) Responses f(x)=−112x−20 f of x is equal to negative 11 halves x minus 20 f(x)=−114x−254 f of x is equal to negative 11 fourths x minus 25 fourths f(x)=112x+35 f of x is equal to 11 halves x plus 35 f(x)=−92x+20
To find the equation of the function, we need to use the given information about the function's values at different x-values.
Let's denote the equation of the function as f(x) = ax + b, where a and b are constants that we need to find.
Given that when x = -5, f(x) = 152:
152 = a*(-5) + b
And given that when x = 3, f(x) = -732:
-732 = a*3 + b
We now have a system of two equations with two unknowns:
152 = -5a + b
-732 = 3a + b
To solve this system of equations, we can subtract the second equation from the first:
(152) - (-732) = (-5a + b) - (3a + b)
884 = -2a
Dividing both sides by -2:
a = -442
Substituting the value of a into one of the equations, we can solve for b:
152 = -5*(-442) + b
152 = 2210 + b
b = -2058
Therefore, the equation of the function is f(x) = -442x - 2058.
None of the provided options matches the equation of the function.