Coordinate Geometry · Topic 4 of 6

📈 Slope & Lines

2 exam question types, fully solved

Slope measures how steep a line is — how much it rises for each step across. Once you can read a slope off an equation, parallel and perpendicular questions become one-liners.

Rise over run, then compare

• Slope from two points: . From a line , the coefficient of is the slope; for it is .

• Parallel lines have equal slopes: .

• Perpendicular lines have slopes whose product is : (each is the negative reciprocal of the other).

• Intercept form cuts the axes at and .

📐Coordinate Plane ExplorerLive calculations as you move points

P1 (x₁, y₁)

x₁

y₁

P2 (x₂, y₂)

x₂

y₂

Distance P1P2√((4−1)² + (5−2)²) = √(9+9)4.243 units

Midpoint M((1+4)/2, (2+5)/2)(2.5, 3.5)

Slope (m)(5−2) / (4−1) = 3/31

Line Equationy = mx + c → y = 1x + (1)y = 1x + 1

The slope of the line through (1, 1) and (4, 7) is .

Q1The slope of the line through (1, 2) and (3, 6) is:

Q2A line parallel to y = 3x + 1 has slope:

Q3Two lines with slopes 2 and −1/2 are:

📚

Real exam questions — Slope & Lines

2 question types · 8 solved examples from real SSC papers

Lines in SSC reward two reflexes: read slope as rise-over-run, and remember that parallel means equal slopes while perpendicular means the slopes multiply to $-1$ . For intercepts, zero out the other coordinate and the crossing point falls out instantly.

How to solve this type

Slope between two points is rise over run:

m=\dfrac{y_2-y_1}{x_2-x_1}

. For a line written as

ax+by+c=0

the slope is

m=-\dfrac{a}{b}

, and for

y=mx+c

the slope is simply the number in front of

x

. A horizontal line

y=k

has slope

0

; a vertical line

x=k

has an undefined slope. Two lines are PARALLEL when their slopes are equal (

m_1=m_2

) and PERPENDICULAR when the product of their slopes is

-1

(

m_1\times m_2=-1

, i.e. flip the fraction and flip the sign).

Find the slope of the line passing through $(2, 3)$ and $(5, 9)$ .

4

2

3

1

What is the slope of the line $y=5$ ?

AundefinedB

5

0

1

Equation of the line parallel to $y=3x+2$ passing through $(1, 4)$ :

y=3x-1

y=3x+1

y=3x+4

y=3x+2

Two lines are perpendicular and one has slope $m_1=2$ . The other slope $m_2$ is:

-2

2

\dfrac{1}{2}

-\dfrac{1}{2}