Question

3 Consider the line y= 3/4x+3. Find the equation of the line that is perpendicular to this line and passes through the point (-8, 6).

Answer 1

`y\text{ = -}(4)/(6)x\text{ - }(14)/(3)`

Step-by-step explanation

We have to find the equation of the line perpendicular to the given line:

`y\text{ = }(3)/(4)x\text{ + 3}`

and passes through the point (-8, 6)

A line perpendicular to another line has a slope that is the negative inverse of the line.

The slope of the given line is 3/4, so the slope of the line we are looking for is -4/3

Now, we use the point slope method to find the equation:

y - y1 = m(x - x1)

where m = slope

(x1, y1) = point the line passes through

So, we have:

`\begin{gathered} y\text{ - 6 = -}(4)/(3)(x\text{ - (-8))} \\ y\text{ - 6 = -}(4)/(3)(x\text{ + 8)} \\ y\text{ - 6 = -}(4)/(3)x\text{ + (-}(4)/(3)\cdot8) \\ y\text{ - 6 = -}(4)/(3)x\text{ - }(32)/(3) \\ \Rightarrow\text{ y = -}(4)/(3)x\text{ - }(32)/(3)\text{ + 6} \\ y\text{ = -}(4)/(6)x\text{ - }(14)/(3) \end{gathered}`

That is the equation of the line.