Answer:
The intercepts are
(8,0,0),(0,-28,0),(0,0,-4)
Step-by-step explanation:
we have
[tex]7x-2y-14z=56[/tex]
step 1
Find the x-intercept
The x-intercept is the value of x when the value of y and z are equal to zero
so
For y=0, z=0
substitute
[tex]7x-2(0)-14(0)=56[/tex]
solve for x
[tex]7x=56[/tex]
[tex]x=8[/tex]
The x-intercept is (8,0,0)
step 2
Find the y-intercept
The y-intercept is the value of y when the value of x and z are equal to zero
so
For x=0, z=0
substitute
[tex]7(0)-2y-14(0)=56[/tex]
solve for y
[tex]-2y=56[/tex]
[tex]y=-28[/tex]
The y-intercept is (0,-28,0)
step 3
Find the z-intercept
The z-intercept is the value of z when the value of x and y are equal to zero
so
For x=0, y=0
substitute
[tex]7(0)-2(0)-14z=56[/tex]
solve for z
[tex]-14z=56[/tex]
[tex]z=-4[/tex]
The y-intercept is (0,0,-4)
therefore
The intercepts are
(8,0,0),(0,-28,0),(0,0,-4)