Question 1202853: -6x+3y=-9
Found 3 solutions by josgarithmetic, Edwin McCravy, math_tutor2020:
Answer by josgarithmetic(39617)   (Show Source):
Answer by Edwin McCravy(20055)  (Show Source):
Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!
Solving for y.
-6x+3y = -9
3y = -9+6x
3y = 6x-9
y = (6x-9)/3
y = (6x)/3-(9/3)
y = 2x-3
A tool like GeoGebra's CAS feature, or WolframAlpha, can be used to verify the answer.
Let's find a few points on this line.
To do so, we plug in values for x to get a paired value for y.
This will give us the (x,y) points needed.
For example, plug in x = 0.
y = 2x-3
y = 2*0-3
y = 0-3
y = -3
The input x = 0 gives the output y = -3.
The point (0,-3) is on the line.
A shortcut is to compare y = 2x-3 to y = mx+b to find that b = -3 is the y intercept.
Now let's try x = 1
y = 2x-3
y = 2*1-3
y = 2-3
y = -1
This produces the ordered pair (1,-1)
Now let's try x = 2
y = 2x-3
y = 2*2-3
y = 4-3
y = 1
This produces the ordered pair (2,1)
Repeat the process however many times you like.
This is a small table of values
Each time x goes up by 1, y goes up by 2.
This is exactly because the slope = 2 = 2/1.
slope = rise/run = 2/1
rise = 2 = go up 2
run = 1 = go right 1
Graph
Graph of -6x+3y=-9, aka y = 2x-3, through the following points
(0, -3)
(1, -1)
(2, 1)
(3, 3)
(4, 5)
To find the x intercept, we plug in y = 0 to solve for x.
y = 2x-3
0 = 2x-3
3 = 2x
2x = 3
x = 3/2
x = 1.5
The x intercept is located at (3/2, 0) aka (1.5, 0).
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