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