What is the equation of the line between (0,2) and (25,-10)?

Jun 25, 2017

The equation of the line is $y = - \frac{12}{25} \cdot x + 2$

Explanation:

The equation of a line is based on two simple questions: "How much $y$ changes when you add $1$ to $x$?" and "How much is $y$ when $x = 0$?"

First, it's important to know that a linear equation has a general formula defined by $y = m \cdot x + n$.

Having those questions in mind, we can find the slope ($m$) of the line, that is how much $y$ changes when you add $1$ to $x$:

$m = \frac{{D}_{y}}{{D}_{x}}$, with ${D}_{x}$ being the difference in $x$ and ${D}_{y}$ being the difference in $y$.

${D}_{x} = 0 - \left(25\right) = 0 - 25 = - 25$
${D}_{y} = 2 - \left(- 10\right) = 2 + 10 = 12$

$m = - \frac{12}{25}$

Now, we need to find ${y}_{0}$, that is the value of $y$ when $x = 0$. Since we have the point $\left(0 , 2\right)$, we know $n = {y}_{0} = 2$.

We now have the slope and the ${y}_{0}$ (or $n$) value, we apply in the main formula of a linear equation:

$y = m \cdot x + n = - \frac{12}{25} \cdot x + 2$