Question

The graphs of the equation y = 4x + 1 and y - kx = 10 are perpendicular when k = _______?

Answer 1

`k=-(1)/(4)`

Explanation:

we have

Line 1

`y=4x+1`

Equation in slope intercept form

The slope is equal to

`m_1=4`

Line 2

`y-kx=10`

`y=kx+10`

Equation in slope intercept form

The slope is equal to

`m_2=k`

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of the slopes is equal to -1)

so

`m_1*m_2=-1`

substitute

`(4)(k)=-1`

`k=-(1)/(4)`