Hey Shelly,
All of these answers are great, but unless you get a better conceptual understanding of the basic parts of a slope intercept equation you will continue to struggle with these equations in the future. In y=mx+b the two parts that we focus on are m, which represents the slope or slant of the line, and b, which represents the y-intercept.
Let's start with b, the y-intercept. The y-intercept-b-, and more specifically the number that will be in the place of b in the actual equation you want to graph, represents a point on the y axis itself. Think of it like an interception in football. The quarterback throws the ball to his player, and the path of the ball is a line from the quarterback to his receiver. To intercept the ball, the defender from the opposing team has to cross that line between the quarterback and his intended receiver. This is like the y-intercept, or b, in our equation. It is the exact point where the line you graph will intersect with the y axis, or vertical axis. When your equation is in slope intercept form, or y-intercept form if you prefer, you can quickly find that point by simply knowing where to look. First you have to be sure the equation is in slope intercept form, here is a quick guide. You can easily tell if an equation is in slope intercept form by looking for a couple of quick details: first, y has to be all by itself on 1 side of the equal sign; second, the x term will be first on the other side, followed by a constant (a number without a variable) that is being added or subtracted.Consider the following example: actual equation y=2x+3
generic form y=mx+b
Notice how the parts line up. Positive 2 is where the m is located in the generic form, and positive 3 is where the b is in the generic form. That means positive 3 is our y-intercept. To locate this on your graph, you simply find the positive 3 on the y axis, which will be up 3 places from the origin of the graph, or where the x and y axis intersect one another. Put a dot there where you found the y- intercept. If the number in place of b were negative, say -3, then you would simply go down on the y axis 3 spaces from the origin. Try looking at a few different slope intercept equations and just spot the y intercepts to get familiar and comfortable with this step, then proceed to the next part: Slope.
The 2 in our example represents the m, or slope of the line. Slope is rise over run, or change in y over change in x. More simply though, it is the slant of the line. Is the line steep, does it rise quickly, or is the line more flat? It is easier for us to use slope in the form of a fraction, so first let's change the 2 into its equivalent fraction, 2/1. 2/1 represents a rise of two (how far you go straight up from your y-intercept), and a run of 1(how far you move left or right from your y intercept). If your slope is positive, you will count up and then to the right(or inversely down and to the left). If your slope is negative you will count up and to the left(or inversely down and to the right). Our slope is positive, so starting from your y-intercept of 3 you will count up 2 times, and then to the right 1 time. That should put you at the coordinates (5,1). Plot this point by putting a dot there, and then simply connect that point to your y-intercept point with a straight line. If you run out of room on your graph counting up for your slope, start over at your y-intercept and go down 2 and to the left 1. I hope this helps. Good Luck
No comments:
Post a Comment