Answer:
<h2>x - 3y = 6</h2>
Step-by-step explanation:
The Standard Form of an equation of a line:
![Ax+By=C](https://tex.z-dn.net/?f=Ax%2BBy%3DC)
We have the x-intercept and the y-intercept
x-intercept is for y = 0
y-intercept is for x = 0
Therefore we have two points: (6, 0) and (0, -2).
The slope-intercept form of an equation of a line:
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
<em>m</em><em> - slope</em>
<em>b</em><em> - y-intercept</em>
The formula of a slope:
![m=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Calculate the slope:
![m=\dfrac{-2-0}{0-6}=\dfrac{-2}{-6}=\dfrac{1}{3}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B-2-0%7D%7B0-6%7D%3D%5Cdfrac%7B-2%7D%7B-6%7D%3D%5Cdfrac%7B1%7D%7B3%7D)
Put it and the value of y-intercept <em>b = -2</em> to the equation of a line:
![y=\dfrac{1}{3}x-2](https://tex.z-dn.net/?f=y%3D%5Cdfrac%7B1%7D%7B3%7Dx-2)
Convert to the standard form:
<em>multiply both sides by (-3)</em>
<em>add x to both sides</em>
![x-3y=6](https://tex.z-dn.net/?f=x-3y%3D6)