Answer:
The value of 'k' is -6.
Step-by-step explanation:
Given:
A line passing through the origin.
The points lying on the line are:
(5, 10) and [tex](-3, k)[/tex]
A line that passes through the origin is given as:
[tex]y=mx[/tex]
Where 'm' is the slope of the line.
Now, (5, 10) lies on the line. So, the point will satisfy the equation.
Therefore, plugging in [tex]x=5,y=10[/tex] in the above equation, we get:
[tex]10=m(5)\\\\10=5m\\\\m=\frac{10}{5}=2[/tex]
So, the slope of the line is 2.
Now, the equation becomes [tex]y=2x[/tex]
Now, point (-3, k) will also satisfy the equation. So, plugging in [tex]x=-3,y=k[/tex], we get
[tex]k=2\times -3\\\\k=-6[/tex]
Therefore, the value of 'k' is -6.
