SSC CGL 2025 Tier-I · 17 September 2025, Shift 1 · Quantitative Aptitude · Question 16 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 13 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

What is the slope of the line 2x + 3y = 6?

(a)−2⁄3
(b)3⁄2
(c)−3⁄2
(d)2⁄3

Answer

Why

Correct — A.
Rewrite 2x + 3y = 6 in the form y = mx + c:

Subtract 2x: 3y = −2x + 6
Divide by 3: y = −(2⁄3)x + 2

The coefficient of x is the slope: m = −2⁄3 → option (a)

Why the others are wrong

(b)
3⁄2 — 3⁄2 is the negative reciprocal of −2⁄3: the slope of a line perpendicular to 2x + 3y = 6, not of the line itself.
(c)
−3⁄2 — −3⁄2 has the right sign but turns the fraction over: it is −b⁄a. The slope of ax + by = c is −a⁄b = −2⁄3.
(d)
2⁄3 — 2⁄3 drops the minus sign. Moving 2x across gives 3y = −2x + 6, so the slope is negative.

Concept

For a line ax + by + c = 0, the slope is m = −a⁄b. It comes from solving for y and reading the coefficient of x.

Here a = 2 and b = 3, so m = −2⁄3. A negative slope means y falls as x rises.

Check with the intercepts: the line meets the axes at (3, 0) and (0, 2), and (0 − 2) ÷ (3 − 0) = −2⁄3. It falls from 2 on the y-axis to 0 at x = 3, the drop a negative slope describes.

Key facts

The slope of ax + by + c = 0 is −a⁄b.
In y = mx + c, m is the slope and c is the y-intercept.
Two perpendicular lines, neither vertical, have slopes whose product is −1.

Study next

Slope of a line through two points: (y₂ − y₁) ⁄ (x₂ − x₁)Slopes of parallel and perpendicular linesThe x- and y-intercepts of ax + by = c

Common traps

Writing the slope as −b⁄a, or as a⁄b without the minus sign: the rule is −a⁄b.
Giving the perpendicular slope 3⁄2 when the question asks for the line's own slope.

15 Sep 2025, 16:00, Quant Q.23 asks for the slope perpendicular to y = −3x + 7, keyed 1⁄3 (option c).

17 Sep 2025, 16:00, Quant Q.16 finds a slope from two points, (2, 3) and (4, 7), keyed 2 (option a).

Related PYQs

No directly related past PYQ was found.

Topic: Graphs of Linear Equations — all 27 SSC CGL questions on it, every solved shift.