Question 250727: I am a little lost at graphing linear equations. could you explain to me the whole concept of how to graph a linear equation?
Found 3 solutions by richwmiller, blwinbbbles, jsmallt9:
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! Linear (line) equations are the easiest equations to do because a line only needs two points.
And there are usually to points that are very easy to find.
They are called the intercepts.
when x=0 and y=0
When x=0 find y and plot (0,y)
when y=0 find x and plot (x,0)
Draw a line connecting them.
Answer by blwinbbbles(106)  (Show Source):
You can put this solution on YOUR website! Ok..a linear equation is expressed by the following y = mx + b
with x and y being the pair cordinates, m = slope and b is the y-intercept (the point where the line crosses the y axis and x = 0)
the standard form is expressed by the following Ax + By = C
These forms can be converted back and forth with simple algebra.
What you will need to graph the line is at least two points. So the easiest way to do the is pick a x and solve for y. I always pick x to be -1, 0 or 1
For example:
if your equation is y = 3x + 2 if I say x = 0, then:
y = 3(0) + 2
y = 2
so your first pair would be (0, 2)
then use x = 1
y = 3(1) + 2
y = 3 + 2
y = 5
then my second pair would be (1, 5)
If I put those on a graph and connect the two points with a line..I have now graphed the linear equation..
Hope this helps
Answer by jsmallt9(3758)  (Show Source):
You can put this solution on YOUR website! If you have two points on the line, then just plot them and draw a line through them. Otherwise...- Find a point on the line. Any point will work but some are better than others. (If (-143, 2035) is a point on the line it will not be convenient to use it.) Often the y-intercept is used. Just pick a value for x and use that value and the equation to find the y for that x.
- Plot the point on the graph.
- Find the slope of the line. There are several common ways of finding the slope of a line:
- If the equation is in (or has been transformed into) slope-intercept form, y = mx + b, the slope is the coefficient of x. (Note: This form is also useful for finding the y-intercept which can be used for the point in steps #1 and #2.)
- If the equation is in (or has been transformed into) Standard form, Ax + By = c, then the slope is -A/B.
- Find a second point on the line and use the slope formula:
- If the slope is not a fraction, write it as a fraction. Any fraction equal to the slope will work. For example, if the slope is 2 we could use any of these: 2/1, 4/2, 6/3, -2/-1, etc.
- Starting from the point you graphed at step #2:
- go up or down based on the numerator of the slope
- go right or left based on the denominator of the slope
- and plot a point where you end up.
- Use a ruler and draw a line through the two points.
Here's a simple example: To graph the equation y = -3x + 1...
1) Find a point on the line. Since this equation is in slope-intercept form we can simply "read" the y-intercept of 1.
2) Plot the point. Plot a point at 1 on the y-axis: (0, 1)
3) Find the slope. We can also "read" the slope from the slope-intercept form: -3.
4) Write the slope as a fraction. We can use -3/1.
5) Starting from our plotted point (0, 1) we go down 3 (because the numerator of the slope is -3) and to the right by 1 (because the denominator of the slope fraction is 1). This should put us at (1, -2). Plot this point.
6) Draw a line through the two points (0, 1) and (1, -2)
If we use 3/-1 for the slope fraction instead of -3/1, we end up with the same line, believe it or not. We start from (0, 1) and go up 3 (because the numerator of the alternate slope fraction is 3) and go to the left by 1 (because the denominator of the alternate slope fraction is -1). This puts us at (-1, 4). Even though the two points we use are different, when we draw a line through each pair, we end up with the same line!
|
|
|
