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Find the equation of the line perpendicular to y = -4x + 3 that also interacts the point (8,1)

Sagot :

Answer:

The answer is "[tex]y = \frac{1}{4}(x-4)[/tex]".

Step-by-step explanation:

Given:

[tex]Line = y= -4x+3 \\ \\point= (8,1)[/tex]

The formula for the standard Equation of a line:

[tex]\to y= mx +c[/tex]

compare the above line value:

[tex]m= -4\\\\c= 3[/tex]

When a line is perpendicular so, the m value is: [tex]= \frac{1}{4}[/tex]

[tex]\to m_1 \times \m_2 = -1\\\\\to -4 \times m_2= -1\\\\\to m_2 = \frac{-1}{-4}\\\\\to m_2= \frac{1}{4}[/tex]

Line equation when one point and m is given:

[tex]\to (y-y_1) = m (x- x_1)\\\\\to (y-1) = \frac{1}{4}(x- 8)\\\\\to 4y-4 = x- 8\\\\\to 4y = x-8+4\\\\\to 4y = x-4\\\\\to y = \frac{1}{4}(x-4)\\[/tex]

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