Question

What is the x- intercept and y- intercept of `y= -4(x+2)`?

Answer 1

The intercept with one axis is simply when the other variable goes to zero. So...

• The `x`-intercept is found by letting `y = 0`.

• The `y`-intercept is found by letting `x = 0`.

The result is shown in this graph:

graph{-4(x+2) [-11.04, 11.46, -10.585, 0.665]}

`(x,y) = overbrace((-2","0))^"x-intercept", overbrace((0","-8))^"y-intercept"`

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Here is how I would do it.

`ul(x-"intercept")`

Let `y = 0` and solve for `x`.

`0 = -4(x + 2)`

`0 = -4x - 8`

`4x = -8`

`x = -8/4 = -2`

As a result, the `x`-intercept is `color(blue)((x,y) = (-2,0))`.

`ul(y-"intercept")`

One way to do this is to notice that in solving for the `x`-intercept, we got

`y = -4x - 8`

The `y = mx + b` form of straight-line equations tells you that `b = -8` is the y-intercept right away, so that the coordinate is `color(blue)((x,y) = (0, -8))` from the work shown above.

Another way to do it is by letting `x = 0`:

`y = -4(0 + 2)`

`= -8`

As a result, the `y`-intercept is `color(blue)((x,y) = (0, -8))`.