Question

Write an equation in slope-intercept form for the line that passes through (-1, 4) and is perpendicular to the graph of the equation: y=3x+5 ?

Answer 1

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

Explanation:

Provided that the line passes through `(-1,4)` and is perpendicular to line `y=3x+5`
We know
The product of gradients of two mutually perpendicular lines is `-1`
So
Let `m_1 = 3`
We have to find `m_2`
So `m_1 ×m_2 =-1`
`or, 3×m_2 =-1`
Hence `m_2 = -1/3`
Choose `m=-1/3`
By point slope forme
`(y-y_1)=m (x-x_1)`
`or, (y-4)=(-1/3)(x-(-1)`
`or, (y-4)=(-1/3)x-(1/3)`
`or, y=(-1/3)x-(1/3)+4` is the required equation.