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What are the intercepts of the equation 18x - 9y + 3z = 18?1. (1, 0, 0), (0, 2, 0), (0, 0, 6)2.(1, 0, 0), (0, -2, 0), (0, 0, 6)3.(6, 0, 0), (0, 3, 0), (0, 0, 1)4.(6, 0, 0), (0, -3, 0), (0, 0, 1)

What Are The Intercepts Of The Equation 18x 9y 3z 181 1 0 0 0 2 0 0 0 621 0 0 0 2 0 0 0 636 0 0 0 3 0 0 0 146 0 0 0 3 0 0 0 1 class=

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SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given equation

[tex]18x-9y+3z=18[/tex]

To get the intercepts, we pick a point and equate the others to zero and then solve for the point.

STEP 2: Get the values of x when y and z are zeroes

[tex]\begin{gathered} 18x-9y+3z=1,z) \\ 18x-9(0)+3(0)=18 \\ 18x-0+0=18,18x=18 \\ Divide\text{ both sides by 18} \\ \frac{18x}{18}=\frac{18}{18} \\ x=1 \\ (x,y,z)\Rightarrow(1,0,0) \end{gathered}[/tex]

STEP 3: Get the values of y when x and z are zeroes

[tex]\begin{gathered} 18x-9y+3z=18_{} \\ \text{Let x and z be 0} \\ 18(0)-9y+3(0)=18 \\ 0-9y+0=18 \\ -9y=18 \\ Divide\text{ both sides by -9} \\ \frac{-9y}{-9}=\frac{18}{-9} \\ y=-2 \\ (x,y,z)\Rightarrow(0,-2,0) \end{gathered}[/tex]

STEP 4: Get the value of z when x and y are zeroes

[tex]\begin{gathered} 18x-9y+3z=18_{} \\ \text{Let x and y be 0} \\ 18(0)-9(0)+3z=18 \\ 3z=18 \\ Divide\text{ both sides by 3} \\ \frac{3z}{3}=\frac{18}{3} \\ z=6 \\ (x,y,z)\Rightarrow(0,0,6) \end{gathered}[/tex]

Hence, the intercepts are:

[tex](1,0,0),(0,-2,0),(0,0,6)[/tex]

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