make the equation slope-intercept form:
subtract 2x from both sides:
4y = -2x + 12
divide by 4 to get y by itself:
y = -1/2x + 3
to make the new line perpendicular to the existing line, completely flip the slope of the line:
y = 2x + 3
Using the z-distribution, it is found that a sample size of 3,385 is required.
<h3>What is a confidence interval of proportions?</h3>
A confidence interval of proportions is given by:

The margin of error is:

In which:
is the sample proportion.
In this problem, we have a 98% confidence level, hence
, z is the value of Z that has a p-value of
, so the critical value is z = 2.327.
We have no prior estimate, hence
is used, which is when the largest sample size is needed. To find the sample size, we solve the margin of error expression for n when M = 0.02, hence:





n = 3,385.
A sample size of 3,385 is required.
More can be learned about the z-distribution at brainly.com/question/25890103
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Ab+ac=a(b+c) or
ba+ca=a(b+c)
c(m-n)+d(m-n)=(m-n)(c+d)