Answer:
x - 3y = 6
Step-by-step explanation:
The Standard Form of an equation of a line:
[tex]Ax+By=C[/tex]
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:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Calculate the slope:
[tex]m=\dfrac{-2-0}{0-6}=\dfrac{-2}{-6}=\dfrac{1}{3}[/tex]
Put it and the value of y-intercept b = -2 to the equation of a line:
[tex]y=\dfrac{1}{3}x-2[/tex]
Convert to the standard form:
[tex]y=\dfrac{1}{3}x-2[/tex] multiply both sides by (-3)
[tex]-3y=-x+6[/tex] add x to both sides
[tex]x-3y=6[/tex]
