Answer:
[tex]y=2x-9[/tex]
Step-by-step explanation:
you have the line
[tex]-3x-6y=17[/tex]
clearing for y:
[tex]-6y=17+3x\\y=\frac{17}{-6} +\frac{3}{-6} x\\y=-\frac{1}{2} x-\frac{17}{6}[/tex]
we have an equation of the form
[tex]y=mx+b[/tex]
the number that accompanies the x is the slope, and the number alone is the intercept with the y-axis
the slope m is:
[tex]m=-\frac{1}{2}[/tex]
i will call the slope of the new line [tex]m_{2}[/tex]
so for two perpendiculares lines we must have:[tex]m*m_{2}=-1[/tex]
and from this we can find the new slope:
[tex]m_{2}=\frac{-1}{m} \\\\m_{2}=\frac{-1}{\frac{-1}{2} } \\m_{2}=2[/tex]
the new slope is 2,
so far we have that the new line is:
[tex]y=2x+b[/tex]
so now we have to find the intercept with the y axis ([tex]b[/tex]) of the new line, since it passes trough (6,3) ---> x = 6 when y = 3
substituting these x and y values in [tex]y=2x+b[/tex]:
[tex]3=2(6)+b\\3=12+b\\b=3-12\\b=-9[/tex]
and finally, the equation of the new line that is perpendicular to the original line is:
[tex]y=2x-9[/tex]
