Answer:
[tex]y=-3x+41[/tex]
Step-by-step explanation:
Equation of a Line
A line of slope m and y-intercept b can be expressed by the equation:
[tex]y=mx+b[/tex]
We are given a line with the equation:
[tex]y=1/3x-5[/tex]
The slope of this line is m1=1/3. To find the slope m2 of a line perpendicular to this one, we use the following equation:
[tex]m_1.m_2=-1[/tex]
Solving for m2:
[tex]\displaystyle m_2=-\frac{1}{m_1}[/tex]
[tex]\displaystyle m_2=-\frac{1}{\frac{1}{3}}=-3[/tex]
Once found the new slope, the required equation has the form:
[tex]y=-3x+b[/tex]
To find b, we use the point (9,14) through which the line passes:
[tex]14=-3(9)+b[/tex]
[tex]b=14+27=41[/tex]
Thus the equation of the line is:
[tex]\boxed{y=-3x+41}[/tex]
