SOLUTION: How do I write a linear function f with the given values A. f(0) = 4,f(5) = 19 B. f (-5) = 32,f(0) = 22

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Question 1175139: How do I write a linear function f with the given values
A. f(0) = 4,f(5) = 19
B. f (-5) = 32,f(0) = 22
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

write a linear function f with the given values

A.
f%28x%29+=+ax%2Bb
if f%280%29+=+4 means for x=0 y=4
4=+a%2A0%2Bb
b=4
if f(5) = 19
19=+a%2A5%2B4
19-4=+5a
15=+5a
a=3
equation is: f%28x%29+=+3x%2B4
B.
use another way to find equation
if f+%28-5%29+=+32, that is point (x%5B1%5D,y%5B1%5D)=(-5,32)
if f%280%29+=+22, that is point (x%5B2%5D,y%5B2%5D)=(0,22)=> this point is y-intercept, so b=22
now find a slope a
a=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
a=%2822-32%29%2F%280-%28-5%29%29
a=-10%2F5
a=-2
equation is: f%28x%29+=+-2x%2B22

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

How do I write a linear function f with the given values
A. f(0) = 4,f(5) = 19
B. f (-5) = 32,f(0) = 22
A.  f(0) = 4, and f(5) = 18 give the coordinate points, (0, 4) and (5, 19)

     

    Point (0, 4) represents the y-intercept, so  

B.  This is done the SAME way as A. You may notice also that its y-intercept is 22.