line j is shown in the xy - plane below. using a simplified fraction, what is the slope (m) of the line…

Explanation:

Step1: Find the slope of line ( j )

Use the slope formula ( m=\frac{y_2 - y_1}{x_2 - x_1} ). Let's take two points on line ( j ), say ((-1,-4)) and ((0, - 1)). Then (m_j=\frac{-1-(-4)}{0 - (-1)}=\frac{-1 + 4}{0+1}=\frac{3}{1}=3).

Step2: Use the perpendicular - slope relationship

If two lines with slopes (m_1) and (m_2) are perpendicular, then (m_1\times m_2=-1). Let (m) be the slope of the line perpendicular to line (j). Since (m_j = 3), we have (3\times m=-1). Solving for (m), we get (m=-\frac{1}{3}).

Answer:

(-\frac{1}{3})