Intercepts — x-intercept, y-intercept — Hinglish notes

2.3.7 · Maths › Coordinate Geometry

WHY — intercepts matter kyun karte hain?

WHAT — intercept kya hota hai? (axis idea se definitions)

HOW — line ki intercept form derive kaise karein

Ek general line $A x + B y = C$ se shuru karo (jahan $A, B, C \neq = 0$ ).

Step 1 — x-intercept find karo. Set $y = 0$ : $A x = C ⟹ x = \frac{C}{A} .$ Yeh step kyun? x-axis par $y = 0$ hota hai, toh $B y$ term gayab ho jaati hai aur sirf $x$ bachta hai.

Step 2 — y-intercept find karo. Set $x = 0$ : $B y = C ⟹ y = \frac{C}{B} .$ Yeh step kyun? y-axis par $x = 0$ hota hai, toh $A x$ term khatam ho jaata hai.

Step 3 — inhe naam do. Maano $a = \frac{C}{A}$ (x-intercept) aur $b = \frac{C}{B}$ (y-intercept).

Step 4 — $a, b$ use karke equation dobara banao. $A x + B y = C$ ko $C$ se divide karo: $\frac{A x}{C} + \frac{B y}{C} = 1 ⟹ \frac{x}{C / A} + \frac{y}{C / B} = 1.$ Toh hum pahunch jaate hain intercept form par:

Figure — Intercepts — x-intercept, y-intercept

Forecast-then-Verify drills

Active-recall flashcards

x-intercept find karne ke liye kaun sa variable zero set karte hain?

y = 0

(point x-axis par hota hai jahan

y = 0

y-intercept find karne ke liye kaun sa variable zero set karte hain?

x = 0

Intercepts

a

aur

b

wali line ki intercept form batao.

\frac{x}{a} + \frac{y}{b} = 1

y = m x + c

mein kaun sa number y-intercept hai?

c

2 x + 3 y = 12

ka x-intercept?

6

, yaani point

(6, 0)

y = x^{2} - 5 x + 6

ka y-intercept?

6

, yaani point

(0, 6)

Origin se jaane wali line intercept form mein kyun nahi likhi ja sakti?

Dono intercepts

0

hain, toh

\frac{x}{a} + \frac{y}{b}

zero se divide karta hai.

Geometrically,

y = f (x)

ke x-intercepts kya hote hain?

f (x) = 0

ke real roots.

Recall Feynman: ek 12-saal ke bacche ko explain karo

Socho ek graph paper par ek road bani hai. Graph paper par do badi roads hain: seedhi wali (x-axis) aur upar-neeche wali (y-axis). Intercept bas woh jagah hai jahan tumhari line un badi roads mein se kisi ek ko touch karti hai. Jab tumhari line seedhi road ko touch karti hai, uska "upar ka amount" ( $y$ ) zero hota hai — toh $y = 0$ karo aur dekho woh kahan jaati hai. Jab woh upar-neeche wali road ko touch karti hai, uska "sideways amount" ( $x$ ) zero hota hai — toh $x = 0$ karo. Bas yahi poora trick hai: jahan road ko touch karo, wahan doosri direction zero set karo.

Connections

Slope-Intercept Form (y = mx + c) — $c$ hi y-intercept hai.
General Equation of a Line (Ax + By = C) — woh source jahan se humne intercept form derive ki.
Roots of a Quadratic — parabola ke x-intercepts uske roots hote hain.
Graphing Straight Lines — do intercepts use karke fast plot karo.
Distance & Coordinates on the Cartesian Plane — kyun "axis par hona" ek coordinate ko $0$ force karta hai.