# How do you write the equation of the line with (0,-1) (3,-5)?

Apr 3, 2016

$\textcolor{b l u e}{y = - \frac{3}{4} x - \frac{11}{4}}$

#### Explanation:

You can use the two point to provide the gradient of the line. Then by substitution of one of these points determine the value of the constant.

standard equation form $\to y = m x + c$

Where $m$ is the gradient and $c$ is the constant of the y intercept

Let Point 1 be ${P}_{1} \to \left({x}_{1} , {y}_{1}\right) \to \left(0 , - 1\right)$
Let point 2 be ${P}_{2} \to \left({x}_{2} , {y}_{2}\right) \to \left(3 , - 5\right)$
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$\textcolor{b l u e}{\text{Determine the gradient}}$

gradient (m) is " "("change in y")/("change in x")

$\implies m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} \to \frac{3 - 0}{- 5 - \left(- 1\right)}$

$\textcolor{b l u e}{\implies m = \frac{3}{-} 4 = - \frac{3}{4}}$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$\textcolor{b l u e}{\text{Determine the constant c}}$

At ${P}_{2} \to y = \left(- \frac{3}{4}\right) x + c \text{ } \to - 5 = \left(- \frac{3}{4}\right) \left(3\right) + c$

$\textcolor{b l u e}{\implies c = - 5 + \frac{9}{4} = - 2 \frac{3}{4} = - \frac{11}{4}}$

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$\textcolor{b l u e}{\text{Putting it all together}}$

$\textcolor{b l u e}{y = - \frac{3}{4} x - \frac{11}{4}}$