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Westkost [7]
3 years ago
13

Someone please please help me with this !

Mathematics
1 answer:
skelet666 [1.2K]3 years ago
3 0

Answer:

4y+x - 16 = 0

Step-by-step explanation:

Given the equaton y - 2 = 4 (x-1)

Get the slope of the line

y - 2 = 4x  - 4

y =  4x - 4 + 2

y = 4x - 2

Since y = mx+b for a line

mx = 4x

m = 4

Slope of a line perpendicular M = -1/4

If the line passes through the point (-4, 5)

The equation in point slope form is expressed as y-y0 = m(x-x0)

Substitute;

y - 5 = -1/4(x-(-4))

y - 5  = -1/4(x+4)

4(y-5) = -(x+4)

4y - 20 = -x-4

4y+x-20+4 = 0

4y+x - 16 = 0

This gives the required equation

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You can convert (1/625) to an exponent, and it would be ideal to have 5 as the base of it because you want your log base to cancel it out. what i usually do in this case is just test out 5^1, 5^2, etc until i find one that matches the number i need. in this case because the number you're trying to work with is a small fraction, you'll want to use NEGATIVE exponents so it'll create a fraction instead of a large whole number:

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so, because they're equal to one another, it'll be waaay easier after you substitute 5^-4 in place of 1/625

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log base 5 of 5 simplifies to 1. subbing in the 5^-4 gets rid of the log for you altogether, and your -4 exponent drops down:

x = -4 is your answer

if the exponent dropping down doesn't make sense to you, you can think of it in another way:

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expand the expression so that the exponent moves in front of the log function:

x = (-4) log₅ 5

then, still, log base 5 of 5 simplifies to 1, so you're left with:

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