Constant of Proportionality & Equation

How the lesson starts: Constant of Proportionality & Equation

The robot factory
Hi there! Welcome to Rivet's robot factory. Every robot needs exactly 5 bolts. Here are 2 robots, and here are their 10 bolts. Rivet wants one magic rule that tells the bolts for any number of robots.
The magic number k
Rivet makes a table. x is robots, y is bolts. 1 robot, 5 bolts. 2 robots, 10. 3 robots, 15. Divide y by x in each row: always 5. That number is k, the constant of proportionality. So the rule is y = 5x.
Worked example
The wheel room table says x = 4 goes with y = 36, and x = 8 goes with y = 72. Find k: 36 ÷ 4 = 9. Check: 72 ÷ 8 = 9. So k = 9 and the equation is y = 9x. Watch out: it's y = 9x, never y = x + 9.