SSC CGL 2025 Tier-I · 18 September 2025, Shift 2 · 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 11 September 2026.

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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.

A line y = mx + 2 passes through (3,8). Find m.

(a)5
(b)4
(c)3
(d)2

Answer

Why

Correct — D. A point lies on a line only if its coordinates satisfy the equation.

Substitute (3, 8) into y = mx + 2: 8 = 3m + 2
Subtract 2: 3m = 6
Divide by 3: m = 2

Check: 2(3) + 2 = 8, as required → option (d)

Why the others are wrong

(a)
5 — m = 5 gives y = 5(3) + 2 = 17 at x = 3, not 8. Five is 8 − 3, a difference of the coordinates, not a slope.
(b)
4 — m = 4 gives y = 4(3) + 2 = 14 at x = 3. The line would pass 6 units above (3, 8).
(c)
3 — m = 3 gives y = 3(3) + 2 = 11, not 8. Three is the point's x-coordinate, not the slope.

Concept

In y = mx + c, m is the slope and c is the y-intercept, where the line crosses the y-axis. Here c = 2, so the line passes through (0, 2).

Any point on the line must satisfy the equation. Put in its x and y, and m is left as the single unknown.

Rise over run gives the same result: from (0, 2) to (3, 8), m = (8 − 2) ÷ (3 − 0) = 6⁄3 = 2.

Key facts

In y = mx + c, m is the slope and c is the y-intercept.
A point (x₁, y₁) lies on a line when substituting it makes both sides equal.
Slope through two points = (y₂ − y₁) ÷ (x₂ − x₁).

Study next

Slope of a line through two given pointsSlopes of parallel and perpendicular lines (m₁m₂ = −1)Point of intersection of two lines

Common traps

Dividing 8 by 3 without first subtracting the intercept 2, which gives 8⁄3.
Swapping the coordinates to (8, 3), which gives 3 = 8m + 2 and m = 1⁄8.

12 Sep 2025, 09:00, Quant Q.24 is the same substitution: y = mx + 5 through (1, 8), keyed m = 3.

19 Sep 2025, 09:00, Quant Q.16 runs it the other way, asking which points lie on y = 4x − 5. (1, −1), (0, −5) and (2, 3) all do, keyed 'All the above'.

Related PYQs

No directly related past PYQ was found.

Topic: Graphs of Linear Equations — all 16 SSC CGL questions on it, every solved shift.