Respuesta :
Answer:
y = (1/3)x - 2
Explanation:
First, we need to identify the slope of the equation 3x + y = 2, so we need to solve for x as:
[tex]\begin{gathered} 3x+y=2 \\ y=2-3x \end{gathered}[/tex]Now, the number beside the variable x is the slope, so the slope is -3
Then, two lines are perpendicular if the product of both slopes is equal to -1. It means that the slope m for our equation should be:
[tex]\begin{gathered} -3\cdot m=-1 \\ m=\frac{-1}{-3}=\frac{1}{3} \end{gathered}[/tex]Now, we can find the equation of the line using the following:
[tex]y=m(x-x_1)+y_1[/tex]Where m is the slope and (x1, y1) is a point on the line. So, replacing my 1/3 and (x1, y1) by (3, -1), we get:
[tex]\begin{gathered} y=\frac{1}{3}(x-3)+(-1) \\ y=\frac{1}{3}x-\frac{1}{3}\cdot3-1 \\ y=\frac{1}{3}x-1-1 \\ y=\frac{1}{3}x-2 \end{gathered}[/tex]Therefore, the equation of the line is: y = (1/3)x - 2
