Give the equation of the line that is parallel to y=-3x+1 and goes through (-5,-6)

1 answer:

8 0

Hi there! The answer is y = -3x - 21

Let's set up the equation of the line step by step! First we need to know that we need to set up an equation in slope-intercept form. We get the following:

y = ax + b.
a represents the slope of the line.
b represents the intercept with the y-axis.

Since our new line is parallel to y = -3x + 1, both lines have the same slope. Therefore the slope of our line, which is represented by a, is -3.

y = -3x + b.
We also know that this line goes through the point (-5, -6) and therefore we can plug in these coordinates into our formula.

-6 = -3 × -5 + b
Simplify

-6 = 15 + b
Subtract 15

-21 = b
Switch sides

b = -21
Hence, y = -3x - 21

~ Hope this helps you!

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F(x) = lnx/x

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$f(x) = \frac{lnx}{x}$

(a) $f'(x) = \frac{d}{dx}[\frac{lnx}{x}]$
Using the quotient rule:
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$f'(x) = \frac{1 - lnx}{x^{2}}$

For maximum, f'(x) = 0;
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$lnx = 1, x = e$

(b) <em>Deduce:
</em> $e^{x} \geq x^{e}, x > 0$
<em>
Soln:</em> Since x = e is the greatest value, then f(e) ≥ f(x) > f(0)
$\frac{ln(e)}{e} \geq \frac{lnx}{x}$
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Now, since x > 0, then we don't have to worry about flipping the signs when multiplying by x.
$\frac{x}{e} \geq lnx$
$x \geq elnx$
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Taking the exponential to both sides will cancel with the natural logarithmic function in the right hand side to produce:
$e^{x} \geq e^{ln(x^{e}})$
$e^{x} \geq x^{e}$ , as required.