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posledela
3 years ago
14

Write the equation of the line that is parallel to the line y=3/2 x +5 and goes through the point (0,7)

Mathematics
1 answer:
zaharov [31]3 years ago
3 0
First, you know that the slope will be the same (3/2).
Plug in the points 0 for x and 7 for y in order to find b.
7=3/2*0+b
b=7
Then put the new slope and y-intercept into the equation:
y=3/2x+7
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Bingel [31]

Answer:

See below.

Step-by-step explanation:

First, notice that this is a composition of functions. For instance, let's let f(x)=\sqrt{x} and g(x)=7x^2+4x+1. Then, the given equation is essentially f(g(x))=\sqrt{7x^2+4x+1}. Thus, we can use the chain rule.

Recall the chain rule: \frac{d}{dx}[f(g(x))]=f'(g(x))\cdot g'(x). So, let's find the derivative of each function:

f(x)=\sqrt{x}=x^\frac{1}{2}

We can use the Power Rule here:

f'(x)=(x^\frac{1}{2})'=\frac{1}{2}(x^{-\frac{1}{2}  })=\frac{1}{2\sqrt{x}}

Now:

g(x)=7x^2+4x+1

Again, use the Power Rule and Sum Rule

g'(x)=(7x^2+4x+1)'=(7x^2)'+(4x)'+(1)'=14x+4

Now, we can put them together:

y'=f'(g(x))\cdot g'(x)=\frac{1}{2\sqrt{g(x)}} \cdot (14x+4)

y'=\frac{14x+4}{2\sqrt{7x^2+4x+1} } =\frac{7x+2}{\sqrt{7x^2+4x+1} }

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