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3 years ago

Write the slop-intercept form of the equation of each line. Please show your work.

Mathematics

1 answer:

solmaris [256]3 years ago

8 0

Slope intercept form is : y = mx + b
as shown the line passes through (0,-3) so the y intercept is -3
The line now is y= mx - 3
the line passes through (4,-2) so substitute x=4, y = -2 to y=mx - 3, we have:
-2 = 4m -3 so m= 1/4

Ans: y = 1/4x -3
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3 years ago

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2 years ago

For the following demand equation compute the elasticity of demand and determine whether the demand is elastic, unitary, or inel

adelina 88 [10]

Answer:

Demand is inelastic at p = 9 and therefore revenue will increase with

an increase in price.

Step-by-step explanation:

Given a demand function that gives q in terms of p, the elasticity of demand is

$E=|\frac{p}{q}\cdot \frac{dq}{dp} |$

If E < 1, we say demand is inelastic. In this case, raising prices increases revenue.
If E > 1, we say demand is elastic. In this case, raising prices decreases revenue.
If E = 1, we say demand is unitary.

We have the following demand equation $D(p)=-\frac{3}{4}p+29$ ; p = 9

Applying the above definition of elasticity of demand we get:

$E(p)=\frac{p}{q}\cdot \frac{dq}{dp}$

where

p = 9
q = $-\frac{3}{4}p+29$
$\frac{dq}{dp}=\frac{d}{dp}(-\frac{3}{4}p+29)$

$\frac{d}{dp}\left(-\frac{3}{4}p+29\right)=-\frac{d}{dp}\left(\frac{3}{4}p\right)+\frac{d}{dp}\left(29\right)\\\\\frac{d}{dp}\left(-\frac{3}{4}p+29\right)=-\frac{3}{4}$

Substituting the values

$E(9)=\frac{9}{-\frac{3}{4}(9)+29}\cdot -\frac{3}{4}\\\\E(9)=\frac{36}{89}\cdot -\frac{3}{4}\\\\E(9)=-\frac{27}{89}\approx -0.30337$

$|E(9)|=|\frac{27}{89}| < 1$

Demand is inelastic at p = 9 and therefore revenue will increase with an increase in price.

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