On putting the values of the point in the equation of line, the value of [tex]k[/tex] is [tex]-\frac{13}{5}[/tex].
When a line passes through a point, the point satisfies the equation of the line.
The line [tex]y = kx +4[/tex] goes through the point [tex](5, -9)[/tex].
So, [tex](5,-9)[/tex] must satisfy the equation of the line.
Put [tex]x=5[/tex] and [tex]y=-9[/tex] in the equation [tex]y = kx +4[/tex].
[tex]-9=k(5)+4[/tex]
[tex]-9=5k+4[/tex]
[tex]-9-4=5k[/tex]
[tex]-13=5k[/tex]
[tex]-\frac{13}{5}=k[/tex]
So, the value of [tex]k[/tex] is [tex]-\frac{13}{5}[/tex].
Learn more here:
https://brainly.com/question/14566987?referrer=searchResults
