Question 607161
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 


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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