What's the value of f(9)?

Question

In a linear function f(4)=6 and f(-2)=14. What's the value of f(9)?

Answer 1

To solve this problem, you first need the function being used.  Since all linear functions take on the form:

 

y = m*x+b

 

 and you're using the same linear function for both number sets, you just have to solve for the slope of the line (m) and the y-intercept value of the line (b).

 

To do this, make a system of equations.  Using 4 and -2 as x values and 6 and 14 as y values, your system should look like this:

 

6 = 4m + b

     14 = -2m + b

 

Now, solve for either the m or b value using substitution or elimination.  If you use substitution, solving the top equation says the value of variable b is 6 - 4m.  Plug this value into the second equation, and then solve for the value of m.  Once you have m, you can plug it into either equation to solve for b.  Finally, plug the 9 into the x position and solve for the value of the function.

Answer 2

You have two points on a line:

(4,6), (-2,14)

 

Find the slope m:

m = (14-6)/(-2-4) = 8/-6 = -4/3

 

We can use the slope intercept form to find the

equation of the line:   y = mx + b 

with m = -4/3, and either of the given points for (x,y).

Let's us (4,6)

 

6 = (-4/3)(4) + b

6 = -16/3 + b

b = 6 + 16/3 = 34/3

 

Your equation of the line is:

y = (-4/3)x + 34/3  or   f(x) = -(4/3)x + 34/3

 

f(9) = (-4/3)(9) + 34/3

= -12 + 34/3

= -36/3 + 34/3

f(9) = - 2/3

 

 

 

Answer 3

I appologize. It seems I was mistaken in my understanding of the question. Please disregard my answer. Michael and Andrew have laid out proper explanations. Thank you.