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

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) (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 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 (,) and (,)

Start with the slope formula

Plug in ,,, (these are the coordinates of given points)

Subtract the terms in the numerator to get . Subtract the terms in the denominator to get

Reduce

So the slope is

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

------Point-Slope Formula------
where is the slope, and is one of the given points

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

Plug in , , and (these values are given)

Distribute

Multiply and to get . Now reduce to get

Add to both sides to isolate y

Combine like terms and to get
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Answer:

So the equation of the line which goes through the points (,) and (,) is:

The equation is now in form (which is slope-intercept form) where the slope is and the y-intercept is

Notice if we graph the equation and plot the points (,) and (,), we get this: (note: if you need help with graphing, check out this solver )

Graph of through the points (,) and (,)

Since the equation is the function is (just replace y with f(x))
Answer by venugopalramana(3286) (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
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