Question

To which of the following types the straight lines represented by $2x+3y-7=0$ and $2x+3y-5=0$ belong?

• A. Parallel to each other
• B. Perpendicular to each other
• C. Inclined at $45°$ to each other
• D. Coincident pair of straight lines

Answer 1

The correct option is A

Parallel to each other

Explanation for the correct option:

Step 1: Rewrite the given equations.

In the question, two lines $2x+3y-7=0$ and $2x+3y-5=0$ are given.

Rewrite the equation of the first line as follows:

$$\begin{gathered} 3y=-2x+7 \\ \Rightarrow y=\frac{-2}{3}x+\frac{7}{3}..1 \end{gathered}$$

Rewrite the equation of the second line as follows:

$$\begin{gathered} 3y=-2x+5 \\ \Rightarrow y=\frac{-2}{3}x+\frac{5}{3}..2 \end{gathered}$$

Step 2: Find the relation between given lines.

We know that the general equation of a line is $y=mx+c...3$.

Where, $m$ is the slope of the line.

$c$ is the $y-$intercept.

$(x,y)$ are the general points on line.

Find the slope $m_1$ of the first line.

From equation $1$ and equation $3$.

$m_1=-\frac{2}{3}$

Find the slope $m_2$ of the first line.

From equation $2$ and equation $3$.

$m_2=-\frac{2}{3}$

Since the slope of both the given lines is equal.

Therefore, the given lines are parallel lines.

Hence, option $A$ is the correct answer.