Question 1006309: If f(x) is a linear function, what is the value of n?
I made a little chart of how the question looks:
x f(x)
–4 -25
-1 -10
n 20
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Step 1) Find the slope of the line through the two points (-4,-25) and (-1,-10)
First point (first row of table):
(x1,y1) = (-4,-25)
Second point (second row of table):
(x1,y1) = (-1,-10)
Slope formula
m = (y2 - y1)/(x2 - x1)
m = (-10 - (-25))/(-1 - (-4))
m = (-10 + 25)/(-1 + 4)
m = (15)/(3)
m = 5
The slope is m = 5
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Step 2) use y = mx+b, the slope found in step 1, and one of the points to find the value of b
m = 5
x = -4
y = -25
The x,y pair is found from the first row
y = mx+b
y = 5x+b ... replace m with 5
y = 5(-4)+b ... replace x with -4
-25 = 5(-4)+b ... replace y with -25; solve for b
-25 = -20+b
-25 = b-20
-25+20 = b-20+20
-5 = b
b = -5
The y intercept is b = -5
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Step 3) Form the equation/function
We found that the slope is m = 5 and the y intercept is b = -5
So y = mx+b turns into y = 5x - 5
Now replace y with f(x) to get f(x) = 5x - 5
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Step 4) Use f(x) = 20 to find the value of x
f(x) = 5x - 5
20 = 5x - 5 ... replace f(x) with 20; solve for x
20+5 = 5x - 5+5
25 = 5x
5x = 25
5x/5 = 25/5
x = 5
The input x value of x = 5 produces the output f(x) value of 20
So n = 5
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Final Answer: n = 5
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