Answer:
[tex]y = 6x+9[/tex]
Step-by-step explanation:
Point slope form:
The equation of line passes through the point [tex](x_1, y_1)[/tex] is given by:
[tex]y-y_1=m'(x-x_1)[/tex] ....[1]
where, m' is the slope
As per the statement:
A given line has the equation
2x+12y=-1
Subtract 2x from both sides we have;
[tex]12y =-2x-1[/tex]
Divide both sides by 12 we have;
[tex]y = -\frac{1}{6}x-\frac{1}{12}[/tex]
On comparing with slope intercept form equation y=mx+b we get;
[tex]m= -\frac{1}{6}[/tex]
We have to find the equation in slope intercept form, of the line that is perpendicular to the given line and passes through the point (0,9)
Since, a line is perpendicular to a given line.
⇒ [tex]m \times m' =-1[/tex]
⇒[tex]m'= \frac{-1}{m}[/tex]
⇒[tex]m' = \frac{-1}{\frac{-1}{6}}[/tex]
Simplify:
m' = 6
Substitute the value of m' and (0, 9) in [1] we have;
[tex]y-9 =6(x-0)[/tex]
⇒[tex]y-9 = 6x[/tex]
Add 9 to both sides we have;
[tex]y = 6x+9[/tex]
Therefore, the equation in slope intercept form, of the line that is perpendicular to the given line and passes through the point (0,9) is, [tex]y = 6x+9[/tex]
