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2 years ago

Find a formula for the linear function passing through the points (-1,14) and (2,-10)

Mathematics

1 answer:

tensa zangetsu [6.8K]2 years ago

5 0

A(-1;14), x=-1, y=14

B(2;-10), x=2, y=-10

General equation for linear function is $y=mx+b$

Let's solve system of equations

$\displaystyle\\\left \{ {{14=-1m+b} \atop {-10=2m+b}} \right. \\\\\left \{ {{b=14+m} \atop {2m+b=-10}} \right. \\\\2m+(14+m)=-10\\3m=-24\\m=-8=>b=14+(-8)=6\\\text{Answer}: y=-8m+6$

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Solve x+2/x-4<0<br><br> A)–4 < x < –2<br> B)–2 < x < 4<br> C)–2 < x < –4

Gelneren [198K]

$Domain:\ x\neq-2\\\\\dfrac{x+2}{x-4}$

Other method:

$\dfrac{x+2}{x-4}$

zeros of numerator and denominator are x = -2 and x = 4.

Look at the second picture.

for x < -2 → x + 2 < 0 and x - 4 < 0

therefore $\dfrac{x + 2}{x - 4}=\dfrac{(-)}{(-)}>0$

for -2 < x < 4 → x + 2 > 0 and x - 4 < 0

therefore $\dfrac{x+2}{x-4}=\dfrac{(+)}{(-)} < 0$

for x > 4 → x + 2 > 0 and x - 4 > 0

therefore $\dfrac{x+2}{x-4}=\dfrac{(+)}{(+)} > 0$

<h3>Answer: B) -2 < x < 4</h3>

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