Question

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

Answer 1

`y=-3x+41`

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=-(1)/(m_1)`

`\displaystyle m_2=-(1)/((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}`