SOLUTION: I think I'm getting the hang of it, I used to be terrified of Math, but at the tender age of 48 (smile), I'm making some headway! Could someone please instruct me on how to gr

Algebra ->  Linear-equations -> SOLUTION: I think I'm getting the hang of it, I used to be terrified of Math, but at the tender age of 48 (smile), I'm making some headway! Could someone please instruct me on how to gr      Log On


   

Question 82928: I think I'm getting the hang of it, I used to be terrified of Math, but at the tender age of 48 (smile), I'm making some headway!
Could someone please instruct me on how to graph the linear equation 6x-7y=8
I can't remember if I asked this already..If so please forgive me!!!
Thank you!!
Found 2 solutions by Nate, jim_thompson5910:
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
6x - 7y = 8
The simplest way to graph a linear function would be in y = mx + b form.
Firstly, we must isolate y.
6x - 7y = 8
6x - 6x - 7y = 8 - 6x
-7y = -6x + 8
-7y/-7 = -6x/-7 + 8/-7
y = (6/7)x - 8/7
Next, we define m and b.
y = mx + b
y = (6/7)x - 8/7
m = 6/7 and b = -8/7
Ok, b is known as the y-intercept, the point that is on the y-axis.
Place a point on -8/7 on the y-axis ... or at (0,-8/7).
m is known as the slope. Positive means up or right and negative means down or left (good reference would be the axies.) The slope once again is 6/7.
The numerator (6) determines up or down. +6 means six units up. The denominator (7) determines left or right. +7 means seven units right. Now, you could also have -6 / -7 ... same way, 6 units down and 7 units left.
~ Proof ~
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2C%286%2F7%29x+-+8%2F7%29

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
6x-7y=8 Start with the given equation

-7y=8-6x Subtract 6x from both sides

y=%288-6x%29%2F-7 Divide both sides by -7

y=%286%2F7%29x-8%2F7 Break up the fraction and rearrange the terms so the x term is first. Now it is in y=mx%2Bb form where m=6%2F7 and b=-8%2F7. So to graph this line, lets plug in point x=-8

Let x=-8
y=%286%2F7%29%28-8%29-8%2F7 Plug in x=-8

y=-48%2F7-8%2F7 Multiply

y=-56%2F7 Combine the fractions

y=-8 Reduce
So we have a point (-8,-8)
Here is the point (-8,-8) plotted on a coordinate system

Let x=6
y=%286%2F7%29%286%29-8%2F7 Plug in x=6

y=36%2F7-8%2F7 Multiply

y=28%2F7 Combine the fractions

y=4 Reduce
So we have a point (6,4). Add this to our graph
Here are the points (6,4) and (-8,-8) plotted on a coordinate system
Now draw a straight line through these points

Graph of y=%286%2F7%29x-8%2F7 with the points (6,4) and (-8,-8)