Question

Find the value of k given that both points lie on a line passing through the origin.

Answer 1

Answer:

$k=-3$

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:

$y=ax$

Where a is the constant of proportionality.

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

$40=5a$

Divide both sides by 5:

$a=8$

Therefore, our equation is:

$y=8x$

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

$-24=8k$

Divide both sides by 8:

$k=-3$

Hence, the value of k is -3.