Question

What is the equation of the line that is perpendicular to `2y = 3x + 12` and passes through the origin?

Answer 1

The equation of the perpendicular line is`" "y=-2/3x`

Explanation:

Given:`" "2y=3x+12`

Divide both sides by 2 giving:

`y=3/2x+6`

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`color(brown)("Known:")`

`color(brown)("standard form of the equation is: "y=mx+c)`

`color(brown)("if the gradient of a straight line graphs is "m)`
`color(brown)("Then the gradient of a line perpendicular to it is " - 1/m)`

The gradient for the given equation is `3/2`

So the gradient of the line perpendicular to this is:

`(-1)xx2/3 = -2/3`

We know this new line passes through`" "(x,y)->(0,0)`

So by substitution:

`y=mx+c" becomes " 0=(-2/3)(0)+c" so "c=0`

Thus the equation of the new line is

`y=-2/3x`