Question

What is the equation of the line that goes through `(3, 7)` and is perpendicular to `8x-3y=-3`?

Answer 1

`y=-3/8x+65/8`

Explanation:

Consider the standard form of `y=mx+c` where `m` is the gradient (slope).

Any line perpendicular to this will have a gradient of `(-1)xx1/m = -1/m`

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given:`" "8x-3y=-3`

We need to convert this into form `y=mx+c`

Add #3y to both sides

`8x=3y-3`

Add 3 to both sides

`8x+3=3y`

Divide both sides by 3

`y=8/3x+1`

Thus `m=8/3`

Thus `-1/m = -3/8`
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So the perpendicular line has the equation: `y=-3/8x+c`

We are told this passes through the point `(x,y)->(3,7)`

So by substituting for `x` and `y` we have

`color(brown)(y=-3/8x+c" "color(blue)(->" "7=-3/8(3)+c)`

`7=-9/8+c`

`c=7+9/8 = 65/8`

Thus we have

`y=-3/8x+65/8`