How do you write an equation in standard form for a line passing through(–2, 1) and (4, 13)?

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Answer 1 · 2015-05-11T20:51:33

The equation is : $y = 2 x + 5$ $y = 2x + 5$

Any linear function has the following form : $y = m x + b$ $y = mx + b$

Firstly, you need to find the slope $m$ $m$ of your line.

It is given by :

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $m = (y_2-y_1)/(x_2-x_1)$ ,

where $(x_{1}, y_{1}) = (- 2, 1)$ $(x_1,y_1)=(-2,1)$ and $(x_{2}, y_{2}) = (4, 13)$ $(x_2,y_2) = (4,13)$ or vice versa.

So $m = \frac{13 - 1}{4 + 2} = 2$ $m = (13-1)/(4+2) = 2$ .

Then, in order to find $b$ $b$ , you have to solve the following equation :

$y_{1} = m x_{1} + b$ $y_1 = mx_1 + b$ or
$y_{2} = m x_{2} + b$ $y_2 = mx_2 + b$

So $1 = 2 \cdot (- 2) + b \Rightarrow b = 5$ $1 = 2*(-2) + b => b = 5$

Now you have the equation of your line :

$y = 2 x + 5$ $y = 2x + 5$