Find the value of k given that both points lie on a line passing through the origin. (k,−24) and (5,40)

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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:

Where a is the constant of proportionality.

Let’s solve for a. We know that when x=5, y=40. So:

Divide both sides by 5:

Therefore, our equation is:

We want to find the value of k such that y=-24. So, subsitute -24 for y and k for x:

Divide both sides by 8:

Hence, the value of k is -3.