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3 years ago

Write the slope-intercept form of the equation that passes through the point (4, -2) and is perpendicular to the line y =4x - 1

Mathematics

1 answer:

ExtremeBDS [4]3 years ago

4 0

Answer:

Step-by-step explanation:

If two lines are perpendicular then the product of theirs slopes is equal -1:

y=m₁x+b₁ ⊥ y=m₂x+b₂ ⇒ m₁×m₂ = -1

y = 4x - 2 ⇒ m₁=4

4×m₂ = -1 ⇒ m₂ = -¹/₄

The line y=-¹/₄x+b passes through point (4, -2) so the equation:

-2 = -¹/₄×4 + b must be true

-2 = -1 + b

b = -1

Therefore equation in slope-intercept form:

y = -¹/₄x - 1

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Step-by-step explanation:

Assuming this question: Use the data to find minium sample size required to estimate population proportion. Margin of error: 0.009, confidence level: 99%, p and q are unknown.

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by: