How do I the linear function of f (x) with slope -2 such that f (-4)=23?

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How do I the linear function of f (x) with slope -2 such that f (-4)=23?

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Answer 1 · 2018-03-24T23:52:14

Hence it is linear it should have the form $f (x) = a \cdot x + b$ $f(x)=a*x+b$
where $a = - 2$ $a=-2$ and $f (- 4) = 23 \Rightarrow 8 + b = 23 \Rightarrow b = 15$ $f(-4)=23=>8+b=23=>b=15$

Hence it is $f (x) = - 2 x + 15$ $f(x)=-2x+15$

Answer 2 · 2018-03-24T23:52:49

$f (x) = - 2 x + 15$ $f(x) = -2x+15$

Explanation:

Start with the slope-intercept form of the equation for a linear function:
$f (x) = m x + b$ $f(x) = mx+b$

Substitute $- 2$ $-2$ for $m$ $m$ (which represents the slope), $- 4$ $-4$ for $x$ $x$ , and $23$ $23$ for $f (x)$ $f(x)$ :
$(23) = (- 2) (- 4) + b$ $(23) = (-2)(-4) + b$

Then simplify and solve for b by subtracting $8$ $8$ from both sides:
$23 = 8 + b$ $23 = 8 + b$
$15 = b$ $15 = b$

Finally, substitute $- 2$ $-2$ for $m$ $m$ and $15$ $15$ for $b$ $b$ into the slope-intercept form of the equation for a linear function:
$f (x) = (- 2) x + (15)$ $f(x) = (-2)x+(15)$
$f (x) = - 2 x + 15$ $f(x) = -2x+15$

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How do I the linear function of f (x) with slope -2 such that f (-4)=23?

2 Answers

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