Question

How do you find a standard form equation for the line `f(-4) = 0` , `f(0) = 2`?

Answer 1

The equation is `x - 2y + 4 = 0`

Explanation:

Consider the basics of function notation: `f(x) = y`. This means that the line is guaranteed to pass through the points `(-4, 0)` and `(0, 2)`. Now, by the slope formula, we have:

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (2 - 0)/(0 - (-4))`

`m = 2/4`

`m = 1/2`

Now we find the equation using point-slope form.

`y- y_1 = m(x - x_1)`

`y - 0 = 1/2(x - (-4))`

`y = 1/2x + 2`

Convert to standard form, which is represented by `Ax +By - C= 0`.

`0 = 1/2x - y + 2`

Since the coefficients must be integers, we must multiply both sides by `2`.

`0 = x - 2y + 4`

Hopefully this helps!