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Question 116277: Can you please help me step by step on this type of linear equation. The equation is x-4y=8. I know I have to rewrite it, I'm not sure how.Also can you help me find plotted numbers for it and graph it.I would like it step by step not leaving anything out. I need to know exactly where you got every number and plot.That's the only way I can learn. Thank you so much it would be a great help.I do have another one ,which is y=4x ,can you do the same for this one?
Thanks again
Laurie
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website!
OK LAURIE, WE'LL TRY TO HELP.
As you know, x-4y=8 represents a straight line. Actually, you don't have to re-write it in order to find points on it and graph it, but you can. We'll do it both ways. The way I like to start is with two columns, one labeled x and the other labeled y. Next, I assign values for x or y and based on the values I assign, I calculate what the value of the other variable is. For example:
Let x=0 then we have:
0-4y=8 divide both sides by -4
y=-2
Now we have one point on the straight line (0,-2)
Now we will let y=0 then we have:
x-0=8 or
x=8
Now we have another point on the straight line (8,0)
Now if we plot the above two points and draw a straight line through them, we will have a graph of the equation and it will look something like this:
On the other hand, if we choose to, we can find more points on the line by continuing to assign values as before. For example:
Let x=4 then we have:
4-4y=8 subtract 4 from both sides
4-4-4y=8-4 collect like terms
-4y=4 divide both sides by -4
y=-1
Now we have another point on the straight line (4,-1)
An we could go on and on assigning values for one variable and calculating the value for the other variable.
Now we will re-write your equation in slope-intercept form and hopefully this will help you to understand the process so you can apply it to other linear equations:
y=mx+b where m is the slope of the line and b is the y-intercept
x-4y=8 subtract x from both sides (we want to isolate y by itself on the left side)
x-x-4y=8-x collect like terms
-4y=8-x divide each term by -4
y=-(8/4)+(x/4) rearranging, we have
y=(x/4)-8/4 or
y=1/4(x)-2 standard slope-intercept form where the slope is (1/4) and the y-intercept is -2
Now lets talk a little about the slope and y-intercept. The y-intercept simply identifies where the line crosses the y axis and we know that when it crosses the y axis, x has to be 0. (In fact, we calculated this earlier when we assigned a value of 0 to x---our point was 0,-2). You, of course, know what slope means---it simply means the ratio of the vertical units to the horizontal units and in this case is 1 to 4. For every one unit that we must go in the y direction to find a point on the line, we must go 4 units in the x direction to find the corresponding x value. When the slope is positive, the line slopes up and to the right; when the slope is negative, the line slopes down and to the right. The slope-intercept form also simplifies the process of assigning values for x and calculating corresponding values for y, as you can see. For example, by inspection, we can see that when x=8, y=0. We now have the two points necessary to draw a graph----------------which we did earlier.
Now lets consider y=4x
First of all, this equation is already in slope-intercept form where the slope is 4 or (4/1) and the y-intercept is 0. This means that one point on the line is (0,0)---IT GOES THROUGH THE ORIGIN!!!
Now we'll let x=1 and we have:
y=4*1 or
y=4
Now we have two points; they are (0,0) and (1,4) and we can now graph the equation
We can generate all the points we want --FAST with this equation
if x=2, then y=8
if x=3, then y=12
if x=4, then y=16
etc.
Here is the plot:
Hope this helps---ptaylor
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