How do you write an equation of a line going through (3,-1) perpendicular to y=4x+1?

Question

Julia Adams · Accepted Answer

#x+4y+1=0#

gradient of the line #y=4x+1# is #4#

Perpendicular means that the gradient of the line perpendicular to the line #y=4x+1# is #-1/4# because the product of the two gradients must equal to #-1# ie #m_1m_2=-1#

Using point gradient formula,

#(y+1)=-1/4(x-3)#

#4y+4=-x+3#

#x+4y+1=0#

Nathan Axel · Answer

undefined To write an equation of a line going through a point (3, -1) and perpendicular to the line y = 4x + 1, you can follow these steps:

1. Determine the slope of the given line y = 4x + 1. In this case, the slope is 4.
2. The slope of a line perpendicular to this line will be the negative reciprocal of 4, which is -1/4.
3. Use the point-slope form of the equation of a line: y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope.
4. Substitute the values x₁ = 3, y₁ = -1, and m = -1/4 into the point-slope form to get the equation of the perpendicular line.

Therefore, the equation of the line perpendicular to y = 4x + 1 and passing through the point (3, -1) is y + 1 = (-1/4)(x - 3).