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

Mar 18, 2016

$y = 2.1 x + 2$

#### 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)

$\frac{0 - 23}{- 1 - 10}$ $= \frac{- 23}{-} 11$ $= 2.1$ (to 1dp)

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

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

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, $\left(10 , 23\right)$ as they are both positive (so it will be easier to calculate).

$m = 2.1 \text{ }$${y}_{1} = 23 \text{ }$ and $\text{ } {x}_{1} = 10$

When we substitute this in, we get:

$y - 23 = 2.1 \left(x - 10\right)$
$y - 23 = 2.1 x - 21$
$y = 2.1 x + 2$

$y = 2.1 x + 2$