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If g is a linear function and g(2)=7 and g(-2)=-1, find g(-5)

If g is a linear function and g(2)=7 and g(-2)=-1, find g(-5)-example-1
User Wamae
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1 Answer

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Since the function is linear, it can be written in slope intercept form which is expressed as

y = mx + c

where

m = slope

c = y intercept

The formula for calculating slope is expressed as

m = (y2 - y1)/(x2 - x1)

From the information given,

g(2) = 7

This means that if x2 = 2, y2 = 7

Also,

g(- 2) = - 1

This means that if x1 = - 2, y1 = - 1

By substituting these values into the formula for calculating slope, we have

m = (7 - - 1)/(2 - - 2) = (7 + 1)/(2 + 2) = 8/4 = 2

We would find the y intercept, c by substituting x = 2, y = 7 and m = 2 into the slope intercept equation. We have

7 = 2 * 2 + c

7 = 4 + c

c = 7 - 4 = 3

By substituting m = 2 and c = 3 into the slope intercept equation, the linear function is

y = 2x + 3

Writing it as a function in terms of g, it is

g(x) = 2x + 3

To find g(- 5), we would substitue x = - 5 into g(x) = 2x + 3, we have

g(- 5) = 2(- 5) + 3 = - 10 + 3

g(- 5) = - 7

User Frediy
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