Question

What is the equation of the line perpendicular to `y=-2/21x` that passes through `(-1,6)`?

Answer 1

The slope of a perpendicular line is the negative reciprocal of the original line.

Explanation:

The slope of the perpendicular line is `21/2`, since the original line has a slope of `-2/21`.

Now we can use point slope form to plug in the point, the slope abs find the slope intercept form equation.

`y - y_1 = m(x - x_1)`

The point (-1,6) is `(x_1, y_1)` while m is the slope.

`y - 6 = 21/2(x - (-1))`

`y - 6 = 21/2x + 21/2`

`y = 21/2x + 21/2 + 6`

`y = 21/2x + 33/2`

Hopefully this helps!

Answer 2

`y=21/2x+33/2`

Explanation:

Given:`" "y=-2/21x` ..............................(1)

Compare to the standard form of`" " y= mx+c`

Where
`m` is the gradient
`x` is the independent variable (can take any value you wish)
`y` is the dependant variable. Its value depend on that of `x`
`c` is a constant that for a straight line graph is the y-intercept

In your equation `c=0` the `"y-intercept "-> y=0`

If `m` is the gradient of the given line then `-1/m` is the gradient of a line perpendicular to it.

`color(blue)("So for the perpendicular line")`

`" "y_("perp") = (-1)xx(-21/2)xx x + c`

`color(blue)(" "y_("perp") = +21/2x + c)`......................(2)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("To determine the value of "c)`

We know that this new line passes through`(x,y)->(-1,6)`

So substitute into equation (2) the values `(x,y)->(color(green)(-1),color(magenta)(6))`

`" "y_("perp") =color(magenta)(6) = +21/2(color(green)(-1)) + c......................(2_a)`

`color(blue)(c=6+21/2 = 33/2)`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Putting it all together")`

The line perpendicular to that given is: `y=21/2x+33/2`