Answer:
[tex]k = -\frac{13}{5}\\[/tex]
Step-by-step explanation:
All points on the line satisfies its corresponding linear equation. If the line, [tex]y = kx +4[/tex], goes through the point, [tex](5,-9)[/tex], then [tex]x = 5[/tex] and [tex]y = -9[/tex] should satisfy the linear equation.
Solving for [tex]k[/tex]:
[tex]y = kx +4 \\ -9 = k(5) +4 \\ -9 = 5k +4 \\ -9 -4 = 5k \\ 5k = -13 \\ k = \frac{-13}{5} \\ k = -\frac{13}{5}[/tex]
