Two letters, two jobs. x goes IN. y comes OUT. We build it from pizza money. Click Next.
Pizza costs $3 each. Delivery is $1, no matter how many.
cost = 3 × pizzas + 1
y = 3x + 1
x = how many pizzas (YOU choose it). y = the cost (the rule answers it). Just like n — but now there are two blanks, so they need two names.
Every part of the equation has a job and a fancy name.
x — the INPUT. The blank YOU fill. How many pizzas? x is just n with a new name — a blank box.
y — the OUTPUT. The answer that comes out. y is not a mystery to hunt — it is the total. Fill x, and y appears.
3 — the COEFFICIENT. Fancy name, simple job: the price of EACH one. It is glued to x, and glued means multiply.
+1 — the CONSTANT. The part that never changes. Delivery is $1 for 1 pizza or 100 pizzas. Constant = "stays the same".
Fill x in. Then watch each order become a point.
Order 5 pizzas: put x = 5 into the rule:
y = 3 × 5 + 1 = $16
Every order is a point (x, y). x first: walk RIGHT. y second: climb UP. That is the whole graph secret.
x and y are NOT two mysteries to solve. In y = 3x + 1, YOU pick x. The rule gives y. One choice, one answer.
Do not swap the point. (2, 7) means x=2, y=7. Right 2, up 7. (7, 2) is a different place!
And remember from the n lesson: 3x means 3 × x. If x = 4, 3x = 12, not 34.
x goes IN, y comes OUT. Coefficient = price of each. Constant = never changes.
Candy costs $5 each, plus a $2 gift bag: y = 5x + 2. What is the 2?
Answer: (C) The constant. The $2 bag costs $2 whether you buy 1 candy or 100.
Full anatomy: y = output (total money) · 5 = coefficient (price of each) · x = input (how many candies) · +2 = constant (the bag). Try x = 3: y = 5×3+2 = $17.