What is the equation of the following line? Be sure to scroll down first to see all answer options. (1/2,3) (0,0)​

Step-by-step explanation:

The equation of the line (-1/2, 3) and (0, 0) is y = -6x

Solution:

Given, two points are (\frac{-1}{2}

2

−1

, 3) and (0, 0)

We have to find the line equation that passes through the given two points.

Now, we know that, line equation that passes through \left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right)(x

1

,y

1

) and (x

2

,y

2

) is given by:

y-y_{1}=\left(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\right)\left(x-x_{1}\right)y−y

1

=(

x

2

−x

1

y

2

−y

1

)(x−x

1

)

Here in our problem, x_{1}=0, y_{1}=0, x_{2}= \frac{-1}{2} \text { and } y_{2}=3x

1

=0,y

1

=0,x

2

=

2

−1

and y

2

=3

Substitute these values in above formula.

\begin{gathered}y-0=\left(\frac{3-0}{\frac{-1}{2}-0}\right)(x-0) \rightarrow y=\frac{3}{\frac{-1}{2}} \times x rightarrow y=3 \times\left(\frac{-2}{1}\right) \times x \rightarrow y=-6 x\end{gathered}

y−0=(

2

−1

−0

3−0

)(x−0)→y=

2

−1

3

×x

→y=3×(

1

−2

)×x→y=−6x

Hence the equation of the line (-1/2, 3) and (0, 0) is y = -6x