Question

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

Answer 1

The answer is "
`y = (1)/(4)(x-4)`".

Explanation:

Given:

`Line = y= -4x+3 \\ \\point= (8,1)`

The formula for the standard Equation of a line:

`\to y= mx +c`

compare the above line value:

`m= -4\\\\c= 3`

When a line is perpendicular so, the m value is:
`= (1)/(4)`

`\to m_1 * \m_2 = -1\\\\\to -4 * m_2= -1\\\\\to m_2 = (-1)/(-4)\\\\\to m_2= (1)/(4)`

Line equation when one point and m is given:

`\to (y-y_1) = m (x- x_1)\\\\\to (y-1) = (1)/(4)(x- 8)\\\\\to 4y-4 = x- 8\\\\\to 4y = x-8+4\\\\\to 4y = x-4\\\\\to y = (1)/(4)(x-4)\\`