To find the x-intercept, which variable do you set to zero?
y=0 (the point lies on the x-axis where y=0).
To find the y-intercept, which variable do you set to zero?
x=0.
State the intercept form of a line with intercepts a and b.
ax+by=1.
In y=mx+c, which number is the y-intercept?
c.
x-intercept of 2x+3y=12?
6, i.e. point (6,0).
y-intercept of y=x2−5x+6?
6, i.e. point (0,6).
Why can't a line through the origin be written in intercept form?
Both intercepts are 0, so ax+by divides by zero.
Geometrically, what are the x-intercepts of y=f(x)?
The real roots of f(x)=0.
Recall Feynman: explain it to a 12-year-old
Imagine a road drawn on graph paper. The graph paper has two big roads: the flat one (x-axis) and the up-down one (y-axis). An intercept is just the spot where your line touches one of those big roads. When your line touches the flat road, its "up amount" (y) is zero — so make y=0 and see where it lands. When it touches the up-down road, its "sideways amount" (x) is zero — so make x=0. That's the whole trick: to find where you touch a road, set the other direction to zero.
Dekho, intercept ka matlab bahut simple hai — jahan pe aapki line ya curve axis ko cross karti hai, wahi point intercept hai. Sabse important trick yeh hai: jab line x-axis ko touch karti hai, tab uska y=0 hota hai (kyunki x-axis pe upar-neeche wali distance zero hoti hai). Aur jab line y-axis ko touch karti hai, tab x=0 hota hai. Bas yahi ek line pura chapter chala deti hai.
Toh formula ratne ki zaroorat nahi. x-intercept nikalna hai? y=0 daal do aur x solve karo. y-intercept nikalna hai? x=0 daal do aur y solve karo. Sabse common galti yeh hoti hai ki students x-intercept ke liye x=0 daal dete hain — galat! Naam axis ka hai, par zero hamesha doosre variable ka hota hai. Yaad rakho: "jis road ko touch karo, doosri road zero."
Intercept form ax+by=1 mein a x-intercept hai aur b y-intercept. Yeh derive kaise hua? General line Ax+By=C ko C se divide kar do, ho gaya. Aur y=mx+c waale form mein toh c seedha y-intercept hai — isliye usko "intercept" kehte hain.
Yeh cheez exam mein bahut kaam aati hai kyunki line ko graph karna ho toh sirf do intercepts nikaalo aur do points join kar do — line ready. Curves (jaise parabola) ke liye x-intercepts uske roots hote hain, jo geometrically dikhata hai ki equation solve karna aur graph cross hona same baat hai. Yeh 80/20 wala concept hai — thoda samajh lo, bahut fayda milega.
