Unit
Graphs of Linear Equations
University of Michigan
Runs his own tutoring company
Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
To unlock all 5,300 videos, start your free trial.
University of Michigan
Runs his own tutoring company
Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
An ellipse is an important conic section and is formed by intersecting a cone with a plane that does not go through the vertex of a cone. The ellipse is defined by two points, each called a focus. From any point on the ellipse, the sum of the distances to the focus points is constant. The position of the foci determine the shape of the ellipse. The ellipse is related to the other conic sections and a circle is actually a special case of an ellipse.
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.