Question

Write an equation of a line perpendicular to y=4x-3 that contains the point (0,7)

Answer 1

Let $k:y=m_1x+b_1$ and $l:y=m_2x+b_2$

$l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}$

We have

$y=4x-3\to m_1=4$

Therefore

$m_2=-\dfrac{1}{4}$

We have the equation of a line:

$y=-\dfrac{1}{4}x+b$

Put the coordinates of the point (0, 7) to the equation of a line:

$7=-\dfrac{1}{4}(0)+b\\\\\7=b\to b=7$

Answer: $\boxed{y=-\dfrac{1}{4}x+7}$