Slope-intercept form of a line is a general formula for the equation of a line. Using the slope-intercept form of a line helps in finding the slope of a line from an equation and the intercept directly from the equation. This is great because it shows how to graph a line using y=mx+b and can be quite useful for applications of linear equations.
Slope intercept form of a line is one of the first ways we deal with a line equation. And basically what it is is, y=mx+b, m is referring to the slope or the steepness of the graph and b is the y intercept. Now remember how we find intercepts is we plug in 0 for the other things. So to find the y intercept, we'll plug in 0 for x, we plug in 0 for x, this goes away leaving us with just y=b. So it's really not any mystery that this is the y intercept, it's just what happens when we would calculate it out. So appreciate for an equation, let me take a look at one. So y=x-2, okay? And I just want to get a, rough sketch to this graph. Get our coordinate grid. Our y intercept is -2. So basically that means we go down the y axis two units, so 1, 2. There's your starting point and from there we know that our slope is 3.
Slope is rise overrun. So that tells us we're going to go up three, 1 up 1, up 2, up 3 then go over one, you get a next point. We could continue on going up 3 over 1, but we really only need two points to get a line. Connect our dots and our line is going to look something like that. It's not exact but it gets an idea of what's going on. So this is the general way of taking a line in slope intercept form, creating a graph.