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2 years ago

Write the equation of the line that is parallel to the line y = 2x + 2 and passes through the point (5, 3)?. .

1 answer:

6 0

The equation of the line given is 2 from the equation y = mx + b where m is the slope. For the lines to be parallel, their slopes should be equal. The equation of the line may also be expressed as,
y - y1 = m(x - x1)
Substituting the values,
y - 3 = 2(x - 5)
The simplified form of the equation is,
y = 2x - 7

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2 years ago

If log2 5 = k, determine an expression for log32 5 in terms of k.

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Answer:

$log_3_2(5)=\frac{1}{5} k$

Step-by-step explanation:

Let's start by using change of base property:

$log_b(x)=\frac{log_a(x)}{log_a(b)}$

So, for $log_2(5)$

$log_2(5)=k=\frac{log(5)}{log(2)}\hspace{10}(1)$

Now, using change of base for $log_3_2(5)$

$log_3_2(5)=\frac{log(5)}{log(32)}$

You can express $32$ as:

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Using reduction of power property:

$log_z(x^y)=ylog_z(x)$

$log(32)=log(2^5)=5log(2)$

Therefore:

$log_3_2(5)=\frac{log(5)}{5*log(2)}=\frac{1}{5} \frac{log(5)}{log(2)}\hspace{10}(2)$

As you can see the only difference between (1) and (2) is the coefficient $\frac{1}{5}$ :

So:

$\frac{log(5)}{log(2)} =k\\$

$log_3_2(5)=\frac{1}{5} \frac{log(5)}{log(2)} =\frac{1}{5} k$

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2 years ago

What is the equation of the line that goes through (−1, −1) and is parallel to y = 6x − 1?

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