Question 607161: Please help!I thought I had the correct answers, but I got them wrong.
find the intercepts and traces for the graph 7x + 3y-z = 42
x-intercept (I had 5,0,0) y-intercept ( I had 0,2,-1) z-intercept (I had 0,0,-1)
xy trace (I had 5,2,0) yz trace (I had (0,2,-1) xz trace (I had 5,0,1)
thank you so much!
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! x-intercept: plug in y = 0 and z = 0 and solve for x
7x + 3y-z = 42
7x + 3(0)-0 = 42
7x + 0 - 0 = 42
7x = 42
x = 42/7
x = 6
So the x-intercept is (6,0,0)
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y-intercept: plug in x = 0 and z = 0 and solve for y
7x + 3y-z = 42
7(0) + 3y-0 = 42
0 + 3y - 0 = 42
3y = 42
y = 42/3
y = 14
So the y-intercept is (0,14,0)
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z-intercept: plug in x = 0 and y = 0 and solve for z
7x + 3y-z = 42
7(0) + 3(0)-z = 42
0 + 0 - z = 42
-z = 42
z = -42
So the z-intercept is (0,0,-42)
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xy trace: Plug in z = 0
7x + 3y-z = 42
7x + 3y - 0 = 42
7x + 3y = 42
So the xy trace is 7x + 3y = 42 (note: this is a line and NOT a point)
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yz trace: plug in x = 0
7x + 3y-z = 42
7(0) + 3y-z = 42
0 + 3y-z = 42
3y-z = 42
So the yz trace is 3y-z = 42
===================================================================================
xz trace: plug in y = 0
7x + 3y-z = 42
7x + 3(0)-z = 42
7x + 0 -z = 42
7x - z = 42
So the xz trace is 7x - z = 42
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