Question

A line in the $xy-$plane passes through the origin and has a slope of $\frac{1}{7}$

Which of the following points lies on the line?

• A. $(0,7)$
• B. $(1,7)$
• C. $(7,7)$
• D. $(14,2)$
• E. $(7,14)$

Answer 1

The correct option is D

$(14,2)$

Step-1 : Explanation for correct option:

For option D: $(14,2)$

Given A line in the $xy-$plane passes through the origin and has a slope of $\frac{1}{7}$
Since $y=\frac{1}{7}x$, check option which points lies on it
Option D : $(14,2)$
$$\begin{gathered} \Rightarrow y=\frac{1}{7}\times 14 \\ \Rightarrow y=2 \end{gathered}$$

So option D is correct
Step -2 : Explanation for incorrect option
Since $y=\frac{1}{7}x$, check option which points lies on it

For Option A : $(0,7)$
$$\begin{gathered} \Rightarrow y=\frac{1}{7}\times 0 \\ \Rightarrow y=0\ne 7 \end{gathered}$$

So option A is incorrect
For Option B : $(1,7)$
$$\begin{gathered} \Rightarrow y=\frac{1}{7}\times 1 \\ \Rightarrow y=\frac{1}{7}\ne 7 \end{gathered}$$

So option B is incorrect
For Option C : $(7,7)$
$$\begin{gathered} \Rightarrow y=\frac{1}{7}\times 7 \\ \Rightarrow y=1\ne 7 \end{gathered}$$

So option C is incorrect
For Option E : $(7,14)$
$$\begin{gathered} \Rightarrow y=\frac{1}{7}\times 7 \\ \Rightarrow y=1\ne 14 \end{gathered}$$

So option $E$ is incorrect

Hence, option $D$ is correct .