Question

Determine and state the equation ofthe line perpendicular to theline 5x-4y=10and passing through the point (10, 6)

Answer 1

Since the line we want if perpendicular to 5x-4y=10, we first want to know the slope of this line. To do that, let's rewrite it in the slope-intercept form:

`\begin{gathered} 5x-4y=10 \\ 4y=5x-10 \\ y=(5x-10)/(4)=(5)/(4)x-(10)/(4) \\ y=(5)/(4)x-(5)/(2) \end{gathered}`

The slope of this line is the linear factor, the one multiplying x: 5/4.

To get the slope of a perpendicular line, we invert it and chenge its sign:

`s_{\text{perpendicular}}=-(1)/(s)=-(4)/(5)`

So, we have, so far:

`y=-(4)/(5)x+b`

We need to find b, and for this we use the point (10,6):

`\begin{gathered} 6=-(4)/(5)\cdot10+b \\ 6=-4\cdot2+b \\ 6=-8+b \\ b=6+8 \\ b=14 \end{gathered}`

So, the euqation of perpedicular line that passes through (10, 6) is:

`y=-(4)/(5)x+14`