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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).

User Zetlen
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1 Answer

3 votes

Answer:

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
$g(x)=-(1)/(3) x+6$.

User Subhasis
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