Question

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)

Answer 1

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

STEP 1: Write the given equation

`18x-9y+3z=18`

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

`\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} \\ (18x)/(18)=(18)/(18) \\ x=1 \\ (x,y,z)\Rightarrow(1,0,0) \end{gathered}`

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

`\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} \\ (-9y)/(-9)=(18)/(-9) \\ y=-2 \\ (x,y,z)\Rightarrow(0,-2,0) \end{gathered}`

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

`\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} \\ (3z)/(3)=(18)/(3) \\ z=6 \\ (x,y,z)\Rightarrow(0,0,6) \end{gathered}`

Hence, the intercepts are:

`(1,0,0),(0,-2,0),(0,0,6)`