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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

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2 Answers

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
 
 
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!