Quick questions on The gradient-intercept formula y = mx + b for HSC Maths Standard 2

An equation only reveals $m$ and $b$ at a glance once it is in the form $y = mx + b$, with $y$ by itself on the left. If it is given any other way, rearrange it first using the same balancing moves you use to solve an equation: whatever you do to one side, do to the other. The goal is always to get $y$ alone.

Going the other way - from a drawn line to its equation - is the reverse of reading $m$ and $b$. You find the two numbers from the picture, then slot them into $y = mx + b$. There are just two things to read off:

The reason $y = mx + b$ matters beyond the classroom is that it models any quantity that starts at a fixed amount and then changes at a steady rate. The most common version in Maths Standard is a cost: a fixed fee plus a charge per unit. The fixed fee is $b$ (the cost before anything happens) and the rate is $m$ (the cost added per unit). The letters are usually changed to fit the situation, but the structure is identical.

When a number multiplies $y$, every term must be divided by it. From $2y = 8x + 6$ the correct result is $y = 4x + 3$, not $y = 4x + 6$.