How do you write an equation of a line given (-20,-10) and (5,15)?

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How do you write an equation of a line given (-20,-10) and (5,15)?

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Answer 1 · 2018-06-20T15:21:12

$(y - - 10) (5 - - 20) = (x - - 20) (15 - - 10)$ $(y- -10)(5 - -20) = (x - -20)(15 - -10)$

$25 (y + 10) = 25 (x + 20)$ $25(y+10)=25(x+20)$

$y = x + 10$ $y=x+10$

Answer 2 · 2018-06-20T15:32:35

Convert the equation into two-point slope form:
$y - y_{1} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} (x - x_{2})$ $y-y_1=(y_2-y_1)/(x_2-x_1) (x-x_2)$ .

The resulting equation being:
$y + 10 = x - 5$ $y+10=x-5$

Explanation:

Let $P_{1}$ $P_1$ be $(- 20, - 10)$ $(-20,-10)$ , with $x_{1} = - 20$ $x_1=-20$ and $y_{1} = - 10$ $y_1=-10$ ,
$P_{2}$ $P_2$ be $(5, 15)$ $(5,15)$ , with $x_{2} = 5$ $x_2=5$ and $y_{2} = 15$ $y_2=15$ ,

By substitution,

$y - (- 10) = \frac{15 - (- 10)}{5 - (- 20)} (x - 5)$ $y-(-10)=(15-(-10))/(5-(-20)) (x-5)$

In evaluating,

$y + 10 = \frac{25}{25} (x - 5)$ $y+10=25/25(x-5)$

Further into:

$y + 10 = x - 5$ $y+10=x-5$ which serves as the final answer.

Source: http://mathworld.wolfram.com/Two-PointForm.html

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How do you write an equation of a line given (-20,-10) and (5,15)?

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