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3 years ago

What is the equation of the line that passes through the point (4,−2) and has a slope of −2?

Mathematics

1 answer:

AVprozaik [17]3 years ago

6 0

Answer:y=-2x+6

Step-by-step explanation:

You want to find the equation for a line that passes through the point (4,-2) and has a slope of -2.

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

To start, you know what m is; it's just the slope, which you said was -2. So you can right away fill in the equation for a line somewhat to read:

y=-2x+b.

Now, what about b, the y-intercept?

To find b, think about what your (x,y) point means:

(4,-2). When x of the line is 4, y of the line must be -2.

Because you said the line passes through this point, right?

Now, look at our line's equation so far: . b is what we want, the -2 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the the point (4,-2).

So, why not plug in for x the number 4 and for y the number -2? This will allow us to solve for b for the particular line that passes through the point you gave!.

(4,-2). y=mx+b or -2=-2 × 4+b, or solving for b: b=-2-(-2)(4). b=6.

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Answer:

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Step-by-step explanation:

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Note: Slope is also termed as the 'rate of change'.

Given that Aron charges an initial service fee of 10$.

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$y = mx+b$

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For example, in one hour i.e. x = 1, the cost 'y' will be:

y = 15x + 10

y = 15(1) + 10

y = 25 + 10

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Therefore, in one hour (x=1), the cost will be: y = $25

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What is the logarithmic form of the solution to 102t = 9?

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Equivalent equations are equations that have the same value

The equation in logarithmic form is $t = \frac{\log(9)}{2}$

<h3>How to rewrite the equation</h3>

The expression is given as:

$10^{2t} = 9$

Take the logarithm of both sides

$\log(10^{2t}) = \log(9)$

Apply the power rule of logarithm

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Divide both sides by log(10)

$2t = \frac{\log(9)}{\log(10)}$

Apply change of base rule

$2t = \log_{10}(9)$

Divide both sides by 2

$t = \frac{\log_{10}(9)}{2}$

Rewrite as:

$t = \frac{\log(9)}{2}$

Hence, the equation in logarithmic form is $t = \frac{\log(9)}{2}$

What is the equation of the line that passes through the point (4,−2) and has a slope of −2?​

What is the equation of the line that passes through the point (4,−2) and has a slope of −2?