SOLUTION: What is the equation for the function in the form f(x)= mx+b? f(1)=1, f(4)=10 Thank you

Algebra ->  Functions -> SOLUTION: What is the equation for the function in the form f(x)= mx+b? f(1)=1, f(4)=10 Thank you      Log On


   

Question 178719: What is the equation for the function in the form f(x)= mx+b?
f(1)=1, f(4)=10
Thank you
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
y is a function of x, or
y+=+f%28x%29
given:
1+=+f%281%29
y+=+1
x+=+1
This gives me the point (1,1)
10+=+f%284%29
y+=+10
x+=+4
This gives me the point (4,10)
f%28x%29+=+mx+%2B+b
y+=+f%28x%29
y+=+mx+%2B+b
For the point (1,1):
(1) 1+=+m%2A1+%2B+b
For the point (4,10):
(2) 10+=+m%2A4+%2B+b
Multiply (1) by 4 and subtract from (2)
(2) 10+=+4m+%2B+b
(1) -4+=+-4m+-+4b
6+=+-3b
b+=+-2
Substitute this in (1)
(1) 1+=+m%2A1+%2B+b
1+=+m+-+2
m+=+3
The equation is f%28x%29+=+3x+-+2 answer
check:
does it go through (1,1)?
1+=+3%2A1+-+2
1+=+1
OK
Does it go through (4,10)?
10+=+3%2A4+-+2
10+=+10
OK