Question

How do you find the x and y intercepts for `9x = 54 - 6y`?

Answer 1

This is in the quadratic question sub group. Did you mean `9x^2=54-6y`?

`y_("intecpt")= 9`

`x=-sqrt6 and x=+sqrt6`

Explanation:

To make the `y` term positive multiply everything on both sides by (-1) giving:

`-9x^2=-54+6y`

Isolate the `y` term: Add 54 to both sides

`54-9x^2=6y`

Isolate `y`: Divide throughout by 6

`54/6-9/6x=y`

Write as per convention

`y=-9/6x^2+54/6`

`y=-3/2x^2+9`
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`color(blue)("Determine the y-intercept")`

This occurs at `x=0`

`y_("intecpt")=-3/2(0^2)+9 = 9`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("Determine the x-intercept")`

This occurs at `y=0`

`x_("intecpt")->y=0=-3/2x^2+9`

`3/2x^2=9`

`x^2=9xx2/3 = 6`

`x=-sqrt6 and x=+sqrt6`

Answer 2

Suppose you really meant `9x=54-6y`

`y_("intercept")=9`

`x_("intercept")=6`

Explanation:

Multiply both sides by (-1)

`-9x=-54+6y`

Add 54 to both sides

`-9x+54=6y`

Divide both side by 6

`-9/6x+54/6=y`

`y=-3/2x+9`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine the y-intercept")`

This occurs at `x=0`

`y=-3/2(0)+9=9`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine the x-intercept")`

This occurs at `y=0`

`y=0=-3/2x+9`

Add `3/2x` to both sides. Moves it to the left of the = sign.

`+3/2x=9`

Multiply both sides by `2/3`

`3/2xx2/3xx x=9xx2/3`

Using the principle that `2xx3=6=3xx2 ->` you can move them around.

`3/3xx2/2xx x=9xx2/3`

`1color(white)("d")xx1xx x=9xx2/3`

`x_("intercept")=6`

color(white)("d")