Question

How do you find the x and y intercepts for `f(x) = -3x-2`?

Answer 1

y-intercept: `-2`

x-intercept: `-2/3`

Explanation:

Note that `f(x)` is equivalent to `y`.

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The y-intercept is the value on the Y-axis where the function crosses the Y-axis. Since the Y-axis is the collection of points where `x=0`, it follows that the y-intercept is the value of the function when `x=0`.

Evaluating `f(x)=-3x-2` when `x=0`:
`color(white)("XXX")f(0)=-3(0)-2=-2`
So the y-intercept is at `(-2)`

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Similarly, the x-intercept is the value of `x` when `y=0` (or equivalently when `f(x)=0`

Evaluating `f(x)=-3x-2` when `f(x)=0`
`color(white)("XXX")0=-3x-2`

`color(white)("XXX")rarr -3x=2`

`color(white)("XXX")rarr x=-2/3`
So the x-intercept is at `(-2/3)`

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