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2 years ago

Find the equation of the line that passes through the given point and has the given slope. (Use x as your variable.)

Mathematics

1 answer:

devlian [24]2 years ago

4 0

Answer:

Slope form of line y = 9

Step-by-step explanation:

m= 3

The y-intercept of the line that passes through the given point (0,9) is

9 = 3(0) + b

b= 9

The equation of the line that passes through the given point (0,9) is

y =mx +b

y = 0 +9

y=9

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2 years ago

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PtichkaEL [24]

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Expand the right side:

$\implies 5x \log 4 = x \log 3 - 2 \log 3$

Move the terms containing x to the left side and factor out x :

$\implies 5x \log 4 - x \log 3 = - 2 \log 3$

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Solve for x by dividing boths ides by 5 log(4) - log(3) :

$\implies \boxed{x = -\dfrac{ 2 \log 3 }{ 5 \log 4 - \log 3 }}$

You can stop there, or continue simplifying the solution by using properties of logarithms:

$\implies x = -\dfrac{ \log 3^2 }{ \log 4^5 - \log 3 }$

$\implies x = -\dfrac{ \log 9 }{ \log 1024 - \log 3 }$

$\implies \boxed{x = -\dfrac{ \log 9 }{ \log \frac{1024}3 }}$

You can condense the solution further using the change-of-base identity,

$\implies \boxed{x = -\log_{\frac{1024}3}9}$

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3 years ago

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