Question

The equation of line c is y=-4/3-4 Line d includes the point (4,-4) and is perpendicular to line c . what is the equation of line d?

Answer 1

Assuming that you mean that the equation of line c is

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

We can deduce that the slope of line c is

`m_c=-(4)/(3)`

since the slope is the coefficient multiplying x in the equation of a line. Since we want line d to be perpendicular to line c, their slope must be in the following relationship:

`m_cm_d=-1 \iff m_d=-(1)/(m_c)=-(1)/(-(4)/(3))=(3)/(4)`

So, line d has slope 3/4 and passes through point (4,-4). Use the equation

`y-y_0=m_d(x-x_0)`

to find the equation of line d, where

`x_0=4,\quad y_0=-4,\quad m_d=(3)/(4)`