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3 years ago

What is the equation of the line that is perpendicular to y = one-fifth x + 4 and that passes through (5,–4)?

Mathematics

1 answer:

zysi [14]3 years ago

4 0

Answer:

y= -5x + 21

Step-by-step explanation:

The equation of the line that passes through (5, -4) and is perpendicular to line y = 1/5x + 4 is y= -5x + 21

The slope that is perpendicular to the slope 1/5x is -5x.

To find a perpendicular slope, you take the negative reciprocal. (so you change the signs (1/5x is positive so now it would be negative) and -5/1 is basically -5)

However, y = -5x + 4 does NOT pass through (5, -4)

But we still have to write the equation in slope intercept form or the equation of the line

The formula for slope- intercept form is : y= mx + b

So we must plug in (m) which is our -5x and for y we look at the coordinates they gave us ----- (5, -4). -4 is our y. In the coordinates we also have x listed which is 5, so we all plug that in.

y = -5x + b (as you can see -5x is plugged in here)

-4 = -5x + b (as you can see -4 is plugged in here)

4 = -5(5) + b (as you can see 5 is plugged in here)

NOW WE MUST SOLVE!

<h3>Isolate B</h3>

-4 = -25 + b

Add 25 from both sides.

-4 = -25 + b

+25 25

----------------

21 = b

We can now plug this into our slope intercept formula---y= mx+ b---to find the equation of the line.

<h2>Therefore, y = -5 x +21</h2>

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4 years ago

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Answer:

There is no exponential function passing through (1,1) and (5,5).

Step-by-step explanation:

We have the following exponential function

$y = Ce^{kt}$

The function passes through these two points:

(1,1): This means that when t = 1, y = 1

(5,5): This means that when t = 5, y = 5.

(1,1)

$y = Ce^{kt}$

$Ce^{k} = 1$

$e^{k} = \frac{1}{C}$

(5,5)

$y = Ce^{kt}$

$5Ce^{k} = 1$

$Ce^{k} = \frac{1}{5}$

From above, we have that:

$e^{k} = \frac{1}{C}$

$C\frac{1}{C} = \frac{1}{5}$

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This means that there is no exponential function passing through (1,1) and (5,5).

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3 years ago

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Read 2 more answers

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hichkok12 [17]

Answer:

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Step-by-step explanation:

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