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I need to know how to graph lines such as x+y=-6 and 4x-5y=3 in the same problem

I need to graph these lines on a graph x+y=-6 and 4x-5y=3

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Brenda G. | Experienced, Passionate Tutor with 3 College DegreesExperienced, Passionate Tutor with 3 Col...
4.3 4.3 (10 lesson ratings) (10)
1
Put each line in the form y=mx +b where m=slope and b= y-intercept (where the line crosses the y-axis).
 
Line 1: x+y=-6 becomes y=-x-6 such that m=-1 and y-intercept = -6
 
Line 2: 4x-5y=3 becomes y=-4/5x+3 where m= 4/5 and y-intercept = -3/5
 
The slope m is the rise over run, or (y2-y1)/(x2-x1) where (x1,y1) and (x2,y2) are any two coordinates on the line.
 
To graph, start drawing each line at the respective y-intercept so one line 1 at (0,-6) and line 2 at (0,-3/5).
 
Then for line 1, the slope is -1 so go down one and right one from (0,-6) to arrive at (1,-7) and proceed the same way in both directions (first point in opposite direction is (-1, -5) ).
 
For line 2, you are at (0,-3/5) [the y-intercept] and the slope is 4/5 so go up 4 and over 5, your next point on line 2 will be ( 5, 3.4), the point in the opposite direction is (-5, -4.6).
 
Let me know if that's clear or if you need more information, Brenda
 
 
Andrew R. | Patient and Knowledgeable Math TutorPatient and Knowledgeable Math Tutor
4.7 4.7 (26 lesson ratings) (26)
0
In order to graph you need to get all the y's to one side of the equation and everything else on the opposite side.
 
You want it in this form: y = mx + b, where m = slope (rise over run) and b = the y-intercept
 
Part (a).
 
x + y = -6  (subtract from both sides)
y = -x - 6
 
When you graph this equation the slope of the line is -1/1 (because -1/1 = -1) and it crosses the y-axis at -6. Plot a point on the y-axis at -6 (because b = -6). Next, from that point go down (rise) 1 space and across (run) 1 space and draw a line through both points and that should give you the graph of x + y = -6.
 
Part (b).
 
4x - 5y = 3  ( subtract 4x from both sides; divide by -5 from both sides)
y = (4/5)x - 3/5
 
When you graph this equation notice that b = -3/5. Therefore the y-intercept of the graph is at (0,-3/5). Next, notice that the m (slope) = 4/5. From the point (0,-3/5) go up (rise) 4 spaces on the y-axis and across (run) 5 spaces and draw your dot. Lastly, connect the two points with a line going through both dots and that should be the graph for 4x - 5y = 3.
 
Hope this helped you!