my next question is how do you graph the lines (stupid question, yes i know but hey its summer) like when it tells you to graph y= -2x + 3
and my last quetion is, is the vertex the number that y is when x is 0?
thanks so much ♥
Answers:
there are several ways to find the slope of a line. First of all, the line must be a straight line to find the slope. The general formula for a linear (straight line) equation is y = mx + b. (Note: this is called the slope - intercept) formula. In this equation, the m (or value in front of the x) is the slope and the b is the y-intercept (where the graph intersects the y axis).
Now, to graph this. b, the y-intercept is 3, so you know that there is the point (0,3) is on the graph of the line. Now you look at the m portion of the equation, again this is the slope. In your case it is a -2. Slope can be explained in several ways--- rise over run, the change in the y coordinates divided by the change in the x coordinates, or given the coordinates of two points (x1, y1) and (x2,y2) as (y2-y1)/(x3-x1). Also, remember when looking at a graph, x is positive going right and negative going left, and y is positive going up and negative going down.
Again, back to your problem. You have the point (0,3) and the slope of -2 (remember -2 can be written as a fraction as
-2/1), so you want to plot at least one other point before drawing your line. Lets do slope as rise over run...in your case a rise of a -2 and a run of 1. I hope you see where it got this. So starting at (0,3) you go down 2 and to the right 1, this should take you to the point (1,2). You now have two points, enough to graph the line. Remember, the line does not just go between these two points, it goes on indefinitely in both directions.
Also, please note that the general formula is y = mx + b; if you are given an equation like 2y = 4x + 8, you first must divide both sides bo 2 to get the equation y = 2x + 4 before you can graph it.
As to your vertex question, I do not understand it. The vertex usually refers to a corner of a polygon, etc. In your case, you have a straight line and there are no corners. The number that y is when x is 0 is called the y-intercept. It is where the line crosses the y axis.
Hope this clarifies how to graph the line. Sorry, it was so wordy, but I wanted you to understand it.
Good Luck
rise over run. the y axis divided by the x axis. the equation that you wrote down the slope is -2 because its in front of the x. there is no vertex on a line. it has to be a parabola or hyperbola. the last question is the y-intercept.
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