Question

what is the equation of a line that passes through the origin and intersects (4,6) in slope

Answer 1

By definition, the equation of a line that passes through the Origin, has the following form:

$y=mx$

Where "m" is the slope of the line.

According to the information given in the exercise, the line passes through this point:

$(4,6)$

You can identify that:

$\begin{gathered} x=4 \\ y=6 \end{gathered}$

Substituting these coordinates into the equation and solving for "m", you can find the slope of the line. This is:

$\begin{gathered} y=mx \\ 6=m(4) \\ \\ \frac{6}{4}=m \\ \\ m=\frac{3}{2} \end{gathered}$

Knowing the slope, you can determine that the equation of this line is:

$y=\frac{3}{2}x$

The answer is: Option D.