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

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Answer 1 · 2017-06-25T15:55:26

The equation of the line is $y = -12/25 * x + 2$

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 $y = m*x + n$ .

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 $x$ :

$m = (D_y)/(D_x)$ , with $D_x$ being the difference in $x$ and $D_y$ being the difference in $y$ .

$D_x = 0-(25) = 0 - 25 = -25$
$D_y = 2-(-10) = 2+10 = 12$

$m = -12/25$

Now, we need to find $y_0$ , that is the value of $y$ when $x=0$ . Since we have the point $(0,2)$ , 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:

$y = m*x + n = -12/25 * x + 2$

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