Answer:
\(y = 6x+9\)
Step-by-step explanation:
Point slope form:
The equation of line passes through the point \((x_1, y_1)\) is given by:
\(y-y_1=m'(x-x_1)\) ....[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;
\(12y =-2x-1\)
Divide both sides by 12 we have;
\(y = -\frac{1}{6}x-\frac{1}{12}\)
On comparing with slope intercept form equation y=mx+b we get;
\(m= -\frac{1}{6}\)
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.
⇒ \(m \times m' =-1\)
⇒\(m'= \frac{-1}{m}\)
⇒\(m' = \frac{-1}{\frac{-1}{6}}\)
Simplify:
m' = 6
Substitute the value of m' and (0, 9) in [1] we have;
\(y-9 =6(x-0)\)
⇒\(y-9 = 6x\)
Add 9 to both sides we have;
\(y = 6x+9\)
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, \(y = 6x+9\)
