In the table, select an equation whose graph is a line perpendicular

Question

In the table, select an equation whose graph is a line perpendicular to the graph of the equation  2x + 3y – 5 = 0 , and an equation whose graph is a line parallel to the graph of the equation  2x + 3y – 5 = 0.  Make only one selection in each column.

T4Star · Answer

Equation of two lines of the form:
ax + by + c = 0
Ax + By + C = 0

They are parallel if:

a = nA and b = nB
This is satisfied in option 4 after rearrangement.

The lines are parallel is (a)(A) + (b)(B) = 0
This is satisfied in option 2

bv8562 · Answer

When two lines are perpendicular to each other then the product of their slopes is equal to -1.
When two lines are parallel to each other then both have the same slope.

2x+3y-5=0 (let's rearrange the equation in the form of the equation of a line)
3y=-2x+5
y=-2x/3+5/3

Slope of line = m1 = -2/3

Therefore, the slope of the perpendicular line must be: 
m1*m2=-1
-2/3*m2=-1
m2=3/2 (option 2)

Slope of line that is parallel to the above line must be same i.e -2/3 (option 5)

Gemmie · Answer

2x + 3y - 5 = 0
=> 3y = -2x + 5
=> y =  \frac{-2}{3} * x + \frac{5}{3}

y = ax + b

Paralle line:  
 
 y = cx + d 
 c = a =  \frac{-2}{3}

Perpendicular 
 
 y = mx + n 
 m * a = -1 
 m =  \frac{3}{2}

egmat · Answer

Let's walk through this step by step.

Step 1: Find the slope of the given line.

The given equation is  2 x +  3 y -  5  =  0 . Rearrange to  slope-intercept form :
 3 y = - 2 x +  5 
y = ( -2/3 )x +  5/3

So the slope is  -2/3 .

Step 2: Determine what slopes we need.

-  Perpendicular lines have slopes that are negative reciprocals . The negative reciprocal of  -2/3  is  3/2 .
-  Parallel lines have the same slope :  -2/3 .

Step 3: Check each option.

Row 1:  y = (x+ 2 )(x- 3 ) — This is a quadratic (parabola), not a line at all. Eliminate.

Row 2:   3 x =  8  +  2 y — Rearrange:  2 y =  3 x -  8 , so y = ( 3/2 )x -  4 . Slope =  3/2 . That's the negative reciprocal of  -2/3 .  This is PERPENDICULAR.

Row 3:  ( 2 x +  3 y)/ 5  — This is just an expression, not an equation (no equals sign with another side). Eliminate.

Row 4:  y = ( 2/3 )x +  5/3  — Slope =  2/3 . This is positive  2/3 , not negative  2/3 . Neither parallel nor perpendicular. Eliminate. ( This is a common trap — watch the sign! )

Row 5:   3 y = - 2 x -  12  — Rearrange: y = ( -2/3 )x -  4 . Slope =  -2/3 . Same slope as the original line.  This is PARALLEL.

Row 6:   3 x +  2 y -  2  =  0  — Rearrange:  2 y = - 3 x +  2 , so y = ( -3/2 )x +  1 . Slope =  -3/2 . This is not the same as  3/2  (wrong sign), so it's neither perpendicular nor parallel.  Another trap!

Final Answer: 
- Perpendicular: Row  2  (slope  3/2 )
- Parallel: Row  5  (slope  -2/3 )

Answer: 2A, 5B

Key Insight:  The key technique here is converting every equation to  y = mx + b form  so you can directly compare slopes.  Also watch out for the distractors — Row  1  isn't even a line, Row  3  isn't even an equation, and Rows  4  and  6  have slopes that look similar to the correct ones but  differ by a sign .

Perpendicular	Parallel
		\(y=(x+2)(x-3)\)
		\(3x=8+2y\)
		\(\frac{(2x+3y)}{5}\)
		\(y=\frac{2}{3}x+\frac{5}{3}\)
		\(3y=-2x-12\)
		\(3x+2y-2=0\)

In the table, select an equation whose graph is a line perpendicular

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Two-part Analysis (TPA) Questions

In the table, select an equation whose graph is a line perpendicular

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards