Question

What is the slope of any line perpendicular to the line passing through `(2,2)` and `(9,5)`?

Answer 1

`-7/3`

Explanation:

the slope of the line passing through the given pts is `(5-2)/(9-2)=3/7`
negative inverse of this slope will be the slope of the line perpendicular to the line joining the given pts.
Hence the slope is `-7/3`

Answer 2

The gradient of the perpendicular line is`" " -7/3`

Explanation:

The standard form equation for a straight line graph is:

`" "y=mx+c`

Where

`x` is the independent variable (may take on any value you wish)

`y` is the dependant variable (its value deponds an what value you give `x`)

`c` is a constant

`m` is the gradient (slope)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("To find the gradient of the given line")`

Let `(x_1,y_1) -> (2,2)`
Let `(x_2,y_2)-> (9,5)`

Then it follows that

`m" "=" " (y_2-y_1)/(x_2-x_1) = (5-2)/(9-2) = 3/7`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine the slope of any line perpendicular to this")`

Given that the first line had gradient `m=3/7`

and that the gradient of the perpendicular line is `(-1)xx 1/m`

Then we have: `(-1)xx7/3=-7/3`