Question

What is the equation of the line between `(0,2)` and `(23,0)`?

Answer 1

`y=(2/23)x+2`

Explanation:

I will solve for slope intercept form, `y=mx+b`

To find the equation given two points, I would use the slope formula to find the slope first

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

`m=(0--2)/(23-0)=2/23`

You do not have to find `b` because it is the `y`-intercept, which we already know is `(0,2)`

`y=(2/23)x+2`

Answer 2

`color(indigo)(2x - 23y = 46, " is the equation in standard form"`

Explanation:

`A (0, 2), B (23, 0)`

Equation of `bar(AB)` is given by the formula

`(y - y_a) / (y_b - y_a) = (x - x_a) / (x_b- x_a)`

`(y - 2) / (0 -2) = (x - 0) / (23 - 0)`

`(y-2) / -2 = x / 23`

`23y - 46 = -2x, " Cross multiplying,"`

`color(indigo)(2x - 23y = 46, " is the equation in standard form"`