The equation of line p is y=−4x+1. Line q is perpendicular to line p and passes through (−4, 1). What is the equation of line q? Write the equation in slope-intercept form with no spaces. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

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Step-by-step explanation:

The question is asking for the slope-intercept equation of a line. The slope-intercept form equation of a line is in the form , where:

For example, the equation of the first line, , is given in slope-intercept form. The slope of that line is while the -intercept of that line is .

Both and need to be found for the second line.

Start by finding the slope of the second line.

Make use of the fact that if two lines in a plane are perpendicular to one another, the product of their slopes would be . In other words, if a line with slope is perpendicular to a line with slope , then . Rearrange to obtain .

In this question, since the slope of the first line is , the slope of the second line (perpendicular to the first line) would be .

Thus, the equation of the second line would be of the form for some constant that needs to be found.

Make use of the fact that the second line goes through the point to find the value of . Since the point is on the second line, the equation of the second line should hold after substituting in and . That is:

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Solve this equation for :

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Therefore, the equation of the second line would be .

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)