SOLUTION: Can you help me with the folowing two questions? Suppose that f is a linear function with slope 4 and that f(3)=5. Find the equation for f. The answer I got was b=-7. Is that right

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations -> SOLUTION: Can you help me with the folowing two questions? Suppose that f is a linear function with slope 4 and that f(3)=5. Find the equation for f. The answer I got was b=-7. Is that right      Log On

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Question 160162: Can you help me with the folowing two questions? Suppose that f is a linear function with slope 4 and that f(3)=5. Find the equation for f. The answer I got was b=-7. Is that right? Do I right the equation f(x)=4(3)-7?
The 2nd question is: Suppose that f is a linear function such that f(3)=5 and f(7)=-4. Find the equation for f. My answer is I think the slope should be -9/4 but what do I do now?

Answer by vleith(2517) About Me  (Show Source):
You can put this solution on YOUR website!
You got the first part correct.
The second problem is a slight variation on the first one.
In the first problem, you were given the slope and a point (3,5). In the second problem, you are just given two points (3,5) and (7, -4). So in the second one, you need to find the slope.
Slope = %28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29
%28-4+-+5%29%2F%287-3%29
-9%2F4
You got that part correct too.
All you need to do now is the same thing you did in the first part
y+=+mx+%2B+b
5+=+%28-9%2F4%29%283%29+%2B+b+
5+%2B+27%2F4+=+b+
47%2F4+=+b
No plug it in
f%28x%29+=+%28-9%2F4%29x+%2B+47%2F4+
Check your answer. Does it work for the point (7, -4)??
-4+=+%28-9%2F4%29%2A7+%2B+47%2F4
-4+=+-63%2F4+%2B+47%2F4
-4+=+-16%2F4
-4+=+-4 so it is true. And the equation is correct.
You were ====> <===== this close. Way to go!