# How do you write an equation of a line given point (0,-4) and (5,-4)?

Jul 12, 2016

$y + 4 = 0.$

#### Explanation:

If we notice that the Y-co-ords. of given two pts. thro. which line passes are same, the eqn. can immediately be written as $: y = - 4 , \mathmr{and} , y + 4 = 0$

This behaviour of pts. on a line occur, when and only when, the line is Horizontal , i.e., line $| |$ to the X-axis.

Otherwise, we may use the formula for the eqn. of a line passing thro. pts. $\left({x}_{1} , {y}_{1}\right) \mathmr{and} \left({x}_{2} , {y}_{2}\right)$ given by, $: \frac{y - {y}_{1}}{x - {x}_{1}} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$ to give,

$\frac{y + 4}{x - 0} = \frac{- 4 + 4}{5 - 0} = 0 \Rightarrow y + 4 = 0.$

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