Question

6. Try It #6 A line passes through the points, (-2, -15) and (2, -3). Find the equation of a perpendicular line that passes through the point, (6, 4).

Answer 1

The equation of the unknown line is
`$g(x)=-(1)/(3) x+6$`.

Explanation:

In the question, it is given that a line passes through (-2,-15) and (2,-3). Another line perpendicular to the first line passes through (6,4).

It is required to find the equation of the second line. of b and substitute all these values to find the equation of second line.

Step 1 of 2

Find the slope of first line.

`$$\begin{aligned}&m_(1)=(-3-(-15))/(2-(-2)) \\&m_(1)=(12)/(4) \\&m_(1)=3\end{aligned}$$`

Therefore, the slope of second line is
`$m_(2)$`.

`$$m_(2)=-(1)/(3)$$`

Step 2 of 2

Substitute the values of
`$m_(2)`,x and g(x) to find the b.

`$$\begin{aligned}&g(x)=m x+b \\&4=-(1)/(3)(6)+b \\&b=4+2 \\&b=6\end{aligned}$$`

Therefore, the equation of the unknown line is
`$g(x)=-(1)/(3) x+6$`.

Step 1 of 2

Find the slope of first line.

`$$\begin{aligned}&m_(1)=(-3-(-15))/(2-(-2)) \\&m_(1)=(12)/(4) \\&m_(1)=3\end{aligned}$$`

Therefore, the slope of second line is
`$m_(2)$`.

`$$m_(2)=-(1)/(3)$$`

Step 2 of 2

Substitute the values of
`$m_(2)`, x and g(x) to find the b.

`$$\begin{aligned}&g(x)=m x+b \\&4=-(1)/(3)(6)+b \\&b=4+2 \\&b=6\end{aligned}$$`

Therefore, the equation of the unknown line is
`$g(x)=-(1)/(3) x+6$`.