SOLUTION: Write an equation for the linear function f satisfying the given conditions. f(3) = 4 and f(0) = 9 I know that these would be looked at as (3,4) and (0,9), but I don't know w

Algebra ->  Linear-equations -> SOLUTION: Write an equation for the linear function f satisfying the given conditions. f(3) = 4 and f(0) = 9 I know that these would be looked at as (3,4) and (0,9), but I don't know w      Log On


   

Question 93107: Write an equation for the linear function f satisfying the given conditions.
f(3) = 4 and f(0) = 9
I know that these would be looked at as (3,4) and (0,9), but I don't know what type of "equation" they're looking for. Thanks so much!!
Found 2 solutions by jim_thompson5910, venugopalramana:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since it is a "linear" function, they are looking for an equation in the form of y=mx%2Bb which forms a line. So we have the points (3,4) and (0,9). Lets find the equation through those points


First lets find the slope through the points (3,4) and (0,9)

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula

m=%289-4%29%2F%280-3%29 Plug in y%5B2%5D=9,y%5B1%5D=4,x%5B2%5D=0,x%5B1%5D=3 (these are the coordinates of given points)

m=+5%2F-3 Subtract the terms in the numerator 9-4 to get 5. Subtract the terms in the denominator 0-3 to get -3


m=-5%2F3 Reduce

So the slope is
m=-5%2F3

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Now let's use the point-slope formula to find the equation of the line:



------Point-Slope Formula------
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and is one of the given points

So lets use the Point-Slope Formula to find the equation of the line

y-4=%28-5%2F3%29%28x-3%29 Plug in m=-5%2F3, x%5B1%5D=3, and y%5B1%5D=4 (these values are given)


y-4=%28-5%2F3%29x%2B%28-5%2F3%29%28-3%29 Distribute -5%2F3

y-4=%28-5%2F3%29x%2B5 Multiply -5%2F3 and -3 to get 15%2F3. Now reduce 15%2F3 to get 5

y=%28-5%2F3%29x%2B5%2B4 Add 4 to both sides to isolate y

y=%28-5%2F3%29x%2B9 Combine like terms 5 and 4 to get 9
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Answer:


So the equation of the line which goes through the points (3,4) and (0,9) is:y=%28-5%2F3%29x%2B9

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-5%2F3 and the y-intercept is b=9

Notice if we graph the equation y=%28-5%2F3%29x%2B9 and plot the points (3,4) and (0,9), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=%28-5%2F3%29x%2B9 through the points (3,4) and (0,9)


Since the equation is y=%28-5%2F3%29x%2B9 the function is f%28x%29=%28-5%2F3%29x%2B9 (just replace y with f(x))

Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
Write an equation for the linear function f satisfying the given conditions.
f(3) = 4 and f(0) = 9
I know that these would be looked at as (3,4) and (0,9), but I don't know what type of "equation" they're looking for. Thanks so much!!
CORRECT...CONTINUE...USE EQN. OF A STRAIGHT LINE(LINEAR) JOINING 2 POINTS (X1,Y1)
AND (X2,Y2) IS
Y-Y1=[(Y2-Y1)/(X2-X1)][X-X1]
Y-4=[(9-4)/(0-3)][X-3]
Y-4=-5(X-3)/3
3Y-12=-5X+15
5X+3Y=27...........OR................
Y=(27-5X)/3
IS THE FUNCTION