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1 year ago

Which line is perpendicular to the line 3y - 4x = 6

Mathematics

1 answer:

Scilla [17]1 year ago

6 0

The equation of the line that is perpendicular to the line 3y - 4x = 6 is: c. 4y + 3x = 8.

<h3>How to Determine the Equation of Lines that are Perpendicular?</h3>

The lines that are perpendicular to each other have slope value of their equation, m, that are negative reciprocals of each other or the product of their slopes is equal to -1.

Given the line 3y - 4x = 6, rewrite the equation in slope-intercept form, y = mx + b, and determine the value of m:

3y = 4x + 6

Divide both sides by 3

3y/3 = 4x/3 + 6/3

y = 4/3x + 2

The slope (m) = 4/3.

The slope of the line that would be perpendicular to the line 3y - 4x = 6, will have a slope of -3/4, which is the negative reciprocal of 4/3.

Rewrite 4y + 3x = 8 in slope-intercept form:

4y = -3x + 8

4y/4 = -3/4x + 8/4

y = -3/4x + 2

The slope of 4y + 3x = 8 is -3/4.

Therefore, the perpendicular line is: c. 4y + 3x = 8.

Learn more about perpendicular lines equation on:

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By using the table 1 attached (See Table 1 attached)

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$\bf m_{yx}=\frac{(\sum y)(\sum x)^2-(\sum x)(\sum xy)}{n\sum x^2-(\sum x)^2}$

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<u>Note:</u> <em>Be careful not to confuse </em>

$\bf \sum x^2$ with $\bf (\sum x)^2$

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Now, to find the line that relates x as a function of y, we simply switch the roles of x and y in the formulas.

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(x=response variable, y=explanatory variable)

$\bf x=m_{xy}y+b_{xy}$

where

$\bf m_{xy}$ is the slope of the line

$\bf b_{xy}$ is the x-intercept

In this case we use these formulas:

$\bf m_{xy}=\frac{(\sum x)(\sum y)^2-(\sum y)(\sum xy)}{n\sum y^2-(\sum y)^2}$

$\bf b_{xy}=\frac{n\sum xy-(\sum x)(\sum y)}{n(\sum y^2)-(\sum y)^2}$

n = 10 is the number of observations taken (pairs x,y)

<u>Note:</u> <em>Be careful not to confuse </em>

$\bf \sum y^2$ with $\bf (\sum y)^2$

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