Question

Find the value of k given that both points lie on a line passing through the origin (5,10)and(-3,k)

Answer 1

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 $(-3, k)$

A line that passes through the origin is given as:

$y=mx$

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 $x=5,y=10$ in the above equation, we get:

$10=m(5)\\\\10=5m\\\\m=\frac{10}{5}=2$

So, the slope of the line is 2.

Now, the equation becomes $y=2x$

Now, point (-3, k) will also satisfy the equation. So, plugging in $x=-3,y=k$, we get

$k=2\times -3\\\\k=-6$

Therefore, the value of 'k' is -6.