Question

What is an equation of the line that is perpendicular to y=−45x+3 and passes through the point (4, 12) ?

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 $y=-45x+3\to m_1=-45$

Therefore

$m_2=-\dfrac{1}{-45}=\dfrac{1}{45}$

We have the equation of a line:

$y=\dfrac{1}{45}x+b$

Put the coordinates of the point (4, 12) to the equation of a line:

$12=\dfrac{1}{45}(4)+b$

$12=\dfrac{4}{45}+b$        subtract $\dfrac{4}{45}$ from both sides

$11\dfrac{41}{45}=b$

Answer: $\boxed{y=\dfrac{1}{45}x+11\dfrac{41}{45}}$

Answer 2

Answer:

y=5/4x + 7

Step-by-step explanation: