Question

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

Answer 1

Answer:

$k=-\frac{1}{4}$

Step-by-step 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

$(4)(k)=-1$

$k=-\frac{1}{4}$