Question

Find the equation of the line that passes through (9,14) and is perpendicular to y= 1/3x-5​

Answer 1

Answer:

$y=-3x+41$

Step-by-step explanation:

Equation of a Line

A line of slope m and y-intercept b can be expressed by the equation:

$y=mx+b$

We are given a line with the equation:

$y=1/3x-5$

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:

$m_1.m_2=-1$

Solving for m2:

$\displaystyle m_2=-\frac{1}{m_1}$

$\displaystyle m_2=-\frac{1}{\frac{1}{3}}=-3$

Once found the new slope, the required equation has the form:

$y=-3x+b$

To find b, we use the point (9,14) through which the line passes:

$14=-3(9)+b$

$b=14+27=41$

Thus the equation of the line is:

$\boxed{y=-3x+41}$