How do you write an equation of a line given (4, 6) and (-7, -3)?

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How do you write an equation of a line given (4, 6) and (-7, -3)?

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Answer 1 · 2016-07-06T02:55:29

Calculate the gradient, substitute in a point on the line, and simplify.

Explanation:

To calculate the gradient, use the formula $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $m=(y_2-y_1)/(x_2-x_1)$ :

$m = \frac{- 3 - 6}{- 7 - 4} = \frac{- 9}{- 11} = \frac{9}{11}$ $m=(-3-6)/(-7-4)=(-9)/-11=9/11$

Now, you can substitute this and one of the given points into the standard formula $y - y_{1} = m (x - x_{1})$ $y-y_1=m(x-x_1)$ :

$y - 6 = \frac{9}{11} (x - 4)$ $y-6=9/11(x-4)$
$y = \frac{9}{11} (x - 4) + 6 = \frac{9 x}{11} - \frac{36}{11} + \frac{66}{11} = \frac{9 x}{11} + \frac{30}{11}$ $y=9/11(x-4)+6=(9x)/11-36/11+66/11=(9x)/11+30/11$
$y = \frac{9 x}{11} + \frac{30}{11}$ $y=(9x)/11+30/11$

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How do you write an equation of a line given (4, 6) and (-7, -3)?

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