The $x$-intercept of a line passing through the points $\left(\frac{-1}{2}, 1\right)$ and $B(1,3)$ is
The $x$-intercept of a line passing through the points $\left(\frac{-1}{2}, 1\right)$ and $B(1,3)$ is
- $-1 / 6$
- $-5 / 4$
- $1 / 3$
- $4 / 3$
Solution
Finding the slope from the given points as:
$\begin{aligned}
& \text {Slope }=\frac{y_2-y_1}{x_2-x_1} \\
& \text {Slope }=\frac{3-1}{1-\left(-\frac{1}{2}\right)} \\
& \text {Slope }=\frac{2}{1+\frac{1}{2}} \\
& \text {Slope }=\frac{2}{\frac{3}{2}}
\end{aligned}$
Slope $=\frac{4}{3}$
Now the equation will be:
$\begin{aligned}
& y=m x+c \\
& y=\frac{4}{3} x+c
\end{aligned}$
Now substituting the point $(1,3)$ into the above equation as:
$\begin{gathered}
3=\frac{4}{3} \times 1+c \\
3-\frac{4}{3}=c \\
\frac{5}{3}=c
\end{gathered}$
So, the equation will be:
$\begin{aligned}
& y=\frac{4}{3} x+c \\
& y=\frac{4}{3} x+\frac{5}{3}
\end{aligned}$
Now to find the $x$-intercept substitute $y=0$ as:
$y=\frac{4}{3} x+\frac{5}{3}$
$0=\frac{4}{3} x+\frac{5}{3}$
$\begin{gathered}
x=-\frac{5}{3} \times \frac{3}{4} \\
x=-\frac{5}{4}
\end{gathered}$
Therefore, the answer is option [2].
Asked in: MHT CET 2021 (20 Sep Shift 2)
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