Math Help - slope-intercept

1. slope-intercept

Ok , so i've got some more homework and i need some help.

Basically in maths we are doing graphs and this is my homework

I have to make a poster explaning how to draw a graph from an equation.
Example (which iam using) y=2x+3.
my extension is that
I have been introduced to gradient and y-intercept. Investigate the connection between the equation of the line and the gradient and y-intercept of the line.

Thank you.

By the way iam 13 so please explain simply because i sometimes dont understand these big words you guys use! haha

thanks youuuuuu xx

2. Slope-Intercept Form

y = 2x + 3 is in "slope-intercept form, which is y = mx + b.

Your slope is in the form of $\frac{change \ in \ y}{change \ in \ x}$
So, from (0, 3), move up 2 units and right 1 unit for $m=\frac{2}{1}$ to locate your second point (1, 5). Draw the line through these two points, and the linear equation is graphed.