From Standard Form Ax + By = C — set the other variable to zero and solve.
📝 10 Questions⏱ ~35 min✅ answers-topic3.html
🐱 Cat + Maths Fun Fact!
A cat's whiskers are exactly as wide as its body — a built-in measuring tool! If Alishba's cat grows at 0.5 kg per month and currently weighs 2 kg, the equation is w = 0.5m + 2. The y-intercept (0, 2) tells you the starting weight. The x-intercept would be where weight = 0 — which doesn't make physical sense (a cat can't weigh nothing!). That's why interpreting intercepts in context is so important. 🐈
✏️ Worked Example — Read This First!
Find the x-intercept and y-intercept of: 3x + 2y = 12
Step-by-Step Solution
1
To find the x-intercept: set y = 0. 3x + 2(0) = 12 → 3x = 12 → x = 4 x-intercept: (4, 0)
2
To find the y-intercept: set x = 0. 3(0) + 2y = 12 → 2y = 12 → y = 6 y-intercept: (0, 6)
3
Check: do both points satisfy the original equation? (4,0): 3(4)+2(0) = 12 ✓ (0,6): 3(0)+2(6) = 12 ✓
x-int: (4, 0) y-int: (0, 6)
💡 Memory trick: x-intercept = "x Alone" → set y = 0. y-intercept = "y Alone" → set x = 0.
Find the x-intercept and y-intercept of 5x + 3y = −15. Then state whether each intercept is positive or negative, and explain what that means on a graph.
A line has x-intercept (4, 0) and y-intercept (0, 6). Use these two points to write the equation in standard form (Ax + By = C). Show all working.
Working space — find the slope first, then write in slope-intercept form, then convert
🐱 Cat Fact + Maths!
Cats sleep on average 12–16 hours per day. If Alishba's cat naps for 14 hours and is active for 10 hours, and you graphed "hours awake" (x) vs "hours asleep" (y), the equation would be x + y = 24 (a day has 24 hours). The x-intercept (24, 0) means: "if the cat is awake all 24 hours, it sleeps 0 hours." The y-intercept (0, 24) means: "if the cat is awake 0 hours, it sleeps all 24 hours." Intercepts describe the boundary cases! 😸