Solved on Dec 22, 2023

Find the solution points for the equation X+Y=6X + Y = 6 and select the correct plot that passes through them.

STEP 1

Assumptions
1. We are working with the linear equation X+Y=6X + Y = 6.
2. We need to create a table of solutions with at least two points to graph the line.
3. We will select values for XX and solve for the corresponding values of YY.

STEP 2

Choose arbitrary values for XX to find corresponding YY values. It's often convenient to choose simple values such as 0, 1, or other integers.

STEP 3

Let's first choose X=0X = 0 and solve for YY.
X+Y=6X + Y = 6 0+Y=60 + Y = 6 Y=6Y = 6

STEP 4

Record the solution pair (X,Y)=(0,6)(X, Y) = (0, 6) in the table.
XY06\begin{array}{c|c} X & Y \\ \hline 0 & 6 \\ \end{array}

STEP 5

Now, choose another value for XX. Let's choose X=1X = 1 and solve for YY.
X+Y=6X + Y = 6 1+Y=61 + Y = 6 Y=61Y = 6 - 1 Y=5Y = 5

STEP 6

Record the solution pair (X,Y)=(1,5)(X, Y) = (1, 5) in the table.
XY0615\begin{array}{c|c} X & Y \\ \hline 0 & 6 \\ 1 & 5 \\ \end{array}

STEP 7

Choose a third value for XX. Let's choose X=2X = 2 and solve for YY.
X+Y=6X + Y = 6 2+Y=62 + Y = 6 Y=62Y = 6 - 2 Y=4Y = 4

STEP 8

Record the solution pair (X,Y)=(2,4)(X, Y) = (2, 4) in the table.
XY061524\begin{array}{c|c} X & Y \\ \hline 0 & 6 \\ 1 & 5 \\ 2 & 4 \\ \end{array}

STEP 9

Now, plot the points from the table on a coordinate plane. The points are (0, 6), (1, 5), and (2, 4).

STEP 10

Draw a straight line through the plotted points. This line represents the equation X+Y=6X + Y = 6.

STEP 11

Verify that the line goes through all the points in the table and that it is indeed a straight line, confirming that the equation represents a linear relationship between XX and YY.

STEP 12

Select the correct plot that shows a straight line passing through the points (0, 6), (1, 5), and (2, 4). This plot correctly represents the equation X+Y=6X + Y = 6.

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