Question

How do you find the important points to graph `y=-2x-3`?

Answer 1

Find the points at which the line crosses the x and y axes.

Explanation:

`x` intercept
When a point is on the `x` axis, we know its `y` value is 0. This means we can make the equation equal to 0 to find `x`.

`0 = -2x -3`

`3 = -2x` (add 3 to both sides)

`3/2 = -x` (divide by 2 on both sides)

`-3/2 = x` (times both sides by -1)

This means `x = -3/2` or `x = -1.5` So our `x` intercept is at the coordinate `(-1.5, 0)`

`y` intercept
On the `y` axis we know the `x` value is equal to 0, so we can substitute this into the equation to find the `y` value.

`y = -2(0) - 3`

`y = -3` (remove anything multiplied by 0)

So we now know our `y` intercept is at `(0,-3)`

So the important points are `(-1.5, 0)` and `(0, -3)`