Answer:
The interceptions are [tex](12,0)[/tex] and [tex](0,-2)[/tex] respectively
Step-by-step explanation:
Given the equation of the line :
[tex]x-6y=12[/tex]
In order to find the interception of the line with the x-axis we need to replace in the equation with ''[tex]y=0[/tex]'' and find the value of x that satisfy this ⇒
If [tex]y=0[/tex] therefore
[tex]x-6y=12\\x-6(0)=12\\x=12[/tex]
So the line intercepts the x-axis in the point [tex](12,0)[/tex]
Finally, in order to find the interception of the line with the y-axis we need to replace in the equation with ''[tex]x=0[/tex]'' and find the value of y that satisfy this ⇒
If [tex]x=0[/tex] therefore
[tex]x-6y=12\\0-6y=12\\-6y=12\\y=\frac{12}{-6} \\y=-2[/tex]
So the line intercepts the y-axis in the point [tex](0,-2)[/tex]
