Question

What is the equation of the line between `(10,23)` and `(-1,0)`?

Answer 1

`y = 2.1x + 2`

Explanation:

The first step here is finding the gradient. We do this by dividing the difference in `y` (vertical) by the difference in `x` (horizontal).
To find the difference, you simply take the original value of `x` or `y` from the final value (use the coordinates for this)

`(0 - 23)/(-1 - 10)` `= (-23)/-11` `= 2.1` (to 1dp)

We can then find the `y` intercept with the formula:

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

Where `m` is the gradient, `y_1` is a `y` value substituted from one of the two coordinates and `x_1` is an `x` value from one of the coordinates you were given (it can be from either of the two as long as it is from the same coordinate as your `y` one).

So, let's use the first coordinate, `(10,23)` as they are both positive (so it will be easier to calculate).

`m=2.1 " "` `y_1 = 23 " "` and `" "x_1 = 10`

When we substitute this in, we get:

`y - 23 = 2.1 (x - 10)`
`y - 23 = 2.1x - 21`
`y = 2.1x + 2`

So, your line equation is:

`y = 2.1x + 2`

Hope this helps; let me know if I can do anything else:)