About when you began learning about slopes, you started using slope-intercept form to write equations for lines. This is exactly what it sounds like, and uses the slope and the y-intercept to construct our equation.
You can think about it this way: if our line 'starts' when x = 0, and moves to the right and left, slope-intercept form gives us the starting place (y-intercept), and our rate of change: how much the graph goes up or down for every unit we move in the x-direction.
We generalize this in Algebra to be y = mx + b, where m is the slope of our line, and b is the y-intercept.
In statistics and calculus, it's often more convenient to look at our line as:
y = b + mx, which means exactly the same thing, but gives us our y-intercept as an initial value.
Extra Help:
EXAMPLE: Write an equation for a line with a slope of 6 and a y-intercept of -5. ANSWER: y = 6x – 5.
Equations in Slope-Intercept Form (AoPS)