Question 1200345: How do you know where to graph these two equations?
3y-2x=6 and -12y+8x=-24
In the textbook, it says that both equations have a y-intercept of (0,2) but I am not understanding HOW they got that?
Found 2 solutions by htmentor, ikleyn:
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! Put the equations in slope-intercept form, y = mx + b where m is the slope and
b is the y-intercept.
3y - 2x = 6. Solve for y:
3y = 2x + 6 -> y = (2/3)x + 2.
I'll leave you to solve the 2nd one yourself.
Answer by ikleyn(52864)  (Show Source):
You can put this solution on YOUR website! .
How do you know where to graph these two equations?
3y-2x=6 and -12y+8x=-24
In the textbook, it says that both equations have a y-intercept of (0,2)
but I am not understanding HOW they got that?
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My explanation consists of two positions.
(1) The equations are
3y - 2x = 6 (1)
-12y + 8x = -24 (2)
Multiply the first equation by (-4). You will get an equivalent equation
and an equivalent system
-12y + 8x = -24 (1')
-12y + 8x = -24 (2')
Now you see that both equations are identical. Hence, they represents
the SAME STRAIGHT LINE on the coordinate plane.
Again: both equations (1'), (2') represent one line.
HENCE, the original equations (1), (2) represent THE SAME unique line.
(2) Now, the point (0,2) is the solution to both equations (1') and (2').
You can CHECK it by substituting x= 0, y= 2 into equations (1') and (2').
But since the point (0,2) is the y-intersection (since x= 0 in it (!) ),
you obtain the ANSWER : the point (0,2) is y-interception to both equations that represent the same line.
Solved.
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From my explanation, you learned two facts
- (1) that the equations represent the same straight line, and
- (2) that the point (0,2) is y-interseption of this line.
You also learned HOW to discover/(to establish) this fact: simply substitute
x= 0, y= 2 into equation/equations and make sure that it is a solution to the given equation.
Now, since the point (0,2) with x= 0 lies on the line, it  y-interception.
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