Answer:
[tex]k=-3[/tex]
Step-by-step explanation:
Since the line passes through the origin, it must be a proportional/direct variation equation.
Direct variation equations have the form:
[tex]y=ax[/tex]
Where a is the constant of proportionality.
Let’s solve for a. We know that when x=5, y=40. So:
[tex]40=5a[/tex]
Divide both sides by 5:
[tex]a=8[/tex]
Therefore, our equation is:
[tex]y=8x[/tex]
We want to find the value of k such that y=-24. So, subsitute -24 for y and k for x:
[tex]-24=8k[/tex]
Divide both sides by 8:
[tex]k=-3[/tex]
Hence, the value of k is -3.
