Respuesta :
Answer:
The equation of the line k is
[tex]y=-\frac{1}{3}x+\frac{5}{3}[/tex]Explanation:
Given that k is perpendicular to line m, defined as:
y = 3x - 1
the slope of k is the negative reciprocal of the slope of line m.
The slope of m is 3
The negative reciprocal of m is -1/3 (this is the slope of k)
Therefore, k is in the form
[tex]y=-\frac{1}{3}x+b[/tex]Since this line passes through the point (x, y) = (-4, 3), we can use this to obtain the value for the y-intercept, b
[tex]\begin{gathered} 3=-\frac{1}{3}(-4)+b \\ \\ 3=\frac{4}{3}+b \end{gathered}[/tex]Solving for b by subtracting 4/3 from both sides
[tex]\begin{gathered} b=3-\frac{4}{3} \\ \\ =\frac{5}{3} \end{gathered}[/tex]The equation is therefore,
[tex]y=-\frac{1}{3}x+\frac{5}{3}[/tex]