# How do you write an equation of a line given (-5,9) and (-4,7)?

Jun 23, 2017

The equation of the line in standard form is $2 x + y = - 1$

#### Explanation:

The slope of the line passing through $\left(- 5 , 9\right) \mathmr{and} \left(- 4 , 7\right)$ is $m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{7 - 9}{- 4 + 5} = - \frac{2}{1} = - 2$

Let the equation of the line in slope-intercept form be $y = m x + c \mathmr{and} y = - 2 x + c$

The point (-5,9) will satisfy the equation . So, $9 = - 2 \cdot \left(- 5\right) + c \mathmr{and} c = 9 - 10 = - 1$

Hence the equation of the line in slope-intercept form is $y = - 2 x - 1.$

The equation of the line in standard form is $2 x + y = - 1$ [Ans]

Jun 23, 2017

Given two points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$
the slope can be calculated as
$\textcolor{w h i t e}{\text{XXX}} m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$
and
once we have a slope, $m$
we can write an equation for the line in slope-point form as either
$\textcolor{w h i t e}{\text{XXX}} y - {y}_{1} = m \left(x - {x}_{1}\right)$
or
$\textcolor{w h i t e}{\text{XXX}} y - {y}_{2} = m \left(x - {x}_{2}\right)$

Using $\left({x}_{1} , {y}_{1}\right) = \left(- 5 , 9\right)$ and $\left({x}_{2} , {y}_{2}\right) = \left(- 4 , 7\right)$
$\textcolor{w h i t e}{\text{XXX}} m = \frac{7 - 9}{\left(- 4\right) - \left(- 5\right)} = - 2$
and
an equation for this line can be written as
$\textcolor{w h i t e}{\text{XXX}} y - 9 = \left(- 2\right) \left(x - \left(- 5\right)\right)$

While this is a completely valid answer, we would normally simplify this and (perhaps) re-write it in "standard" form:
$\textcolor{w h i t e}{\text{XXX}} y - 9 = - 2 x - 10$

$\textcolor{w h i t e}{\text{XXX}} 2 x + y = - 1$

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It would be a good idea to verify that this equation is valid for the two given points, so:
{: ("Substituting: "(-5,9)" for " (x,y),color(white)("xxxxxx"),"Substituting: "(-4,7)" for " (x,y)), (" in " 2x+y=-1,," in " 2x+y=-1), ("",,""), (rarr2*(-5)+9=-1,,rarr2*(-4)+7=-1), ("correct",,"correct") :}