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3 years ago

What is the equation of the line that is parallel to the line y=2x+3 and passes through the point (-2,1)

Mathematics

1 answer:

Lerok [7]3 years ago

3 0

Answer:

y= 2x+5

Step-by-step explanation:

The equation of a line is usually written in the form of y=mx+c, where m is the gradient and c is the y-intercept.

Parallel lines have the same gradient. Hence m=2.

Subst. m=2 into the equation:

y=2x +c

Now substitute a coordinate.

When x= -2, y=1,

1= 2(-2) +c

1= -4 +c

c= 1 +4

c=5

Thus, the equation of the line is y= 2x +5.

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SOLUTION

From the question, we are told that y varies inversely as x

This is mathematically written as

$\begin{gathered} y\propto\frac{1}{x} \\ \propto\text{ is a sign of proportionality } \end{gathered}$

Now, we will remove the proportionality sign and replace it with equal to sign =

If we do this, we will intoduce a constant k

$\begin{gathered} y\propto\frac{1}{x} \\ y=k\times\frac{1}{x} \\ y=\frac{k}{x} \end{gathered}$

So we have the formula

$y=\frac{k}{x}$

We will substitute the values of x for 10 and y for 8 into the formula to get k, we have

$\begin{gathered} y=\frac{k}{x} \\ 8=\frac{k}{10} \\ k=8\times10 \\ k=80 \end{gathered}$

Now, we will substitute k for 80 back into the formula to get the inverse function, we have

$\begin{gathered} y=\frac{k}{x} \\ y=\frac{80}{x} \end{gathered}$

Hence the answer is option C

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1 year ago

List all of the subsets of the set {1, 3, 5}

Lostsunrise [7]

Answer:

Step-by-step explanation:

( ),(1),(3),(5),(1,3),(1,5),(3,5)

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3 years ago

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SCORPION-xisa [38]

Answer:

Step-by-step explanation:

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3 years ago

A television set cost $350 cash when bought on hire purchase a deposit of $35 is required followed by 12 monthly payments of $30

r-ruslan [8.4K]

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www.imsorryineedpoints.orgStep-by-step explanation:

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3 years ago

The cost of tuition at a college is $12,000 and is increasing at the rate of 6% each year. Use exponential function to find the

Gnesinka [82]

Answer:

The cost of tuition fee after 4 years is $15,149.72.

Step-by-step explanation:

Exponential function:

$A=P(1+r)^n$

A= the amount after n years

P= Initial amount

r= rate of increasing

n= time in years

The cost of tuition at a college is $12,000. It is increasing at the rate of 6% each year.

Here, P= $12,000, r= 6%= 0.06, n= 4 years.

$\therefore A=12,000(1+0.06)^4$

$\Rightarrow A= 12000(1.06)^4$

=$15,149.72

The cost of tuition fee after 4 years is $15,149.72.

7 0

4 years ago