Question

Which of the following lines pass through the point (3,-2)?

• A. $2x+3y=0$
• B. $x+y=1$
• C. $x-2y=7$
• D. All of the above.

Answer 1

The correct option is D All of the above.

A line passes through a point if that point satisfies the equation of the line.

Given point (3, -2)

(i) Line represented by the equation $2x+3y=0$

$2\times 3+3\times (-2)=0$

(ii) Line represented by the equation $x+y=1$

$3+(-2)=1$

(iii) Line represented by the equation $x-2y=7$

$3-(2\times (-2\left)\right)=3+4=7$

Since in all the three cases LHS = RHS, the point (3, -2) satisfies all the given equations.
Therefore, all the given lines pass through the point (3,-2).