y = 2x + 3 (saving money story)
Imagine you already have three dollars in your piggy bank, and you save two more dollars every week.
Let's graph it. The bottom axis is weeks, the side axis is dollars.
Before any weeks pass, you already have three dollars. So we mark the point zero, three.
That spot where our line meets the y-axis has a name — it's b, the y-intercept.
Now one week passes. We move one step to the right…
…and because you saved two dollars, we go two steps up.
After one week, you have five dollars. Plot one, five.
Connect the points and extend the line. Every point on it shows your savings on some week.
We can write this whole story as one short equation: y equals two x plus three.
The two is m — the slope. It tells us how fast the dollars grow each week.
The three is b — the y-intercept. It's the starting amount, what you have when x is zero.
So y equals m x plus b means: start at b, then climb by m every step. That's slope-intercept form!