Math  /  Algebra

QuestionComplete the table for the equation x+2y=9x+2 y=9, and graph the equation. \begin{tabular}{|c|c|} \hlinexx & yy \\ \hline 0 & 4.5 \\ \hline 9 & 0 \\ \hline 5 & 2 \\ \hline 1 & 4 \\ \hline \end{tabular}
Use the graphing tool to graph the line using two points. \square Click to enlarge riranh
Selected: \square none \square ζ\zeta V \square \cup \square C Delete Clear ?? Clear all Check answer

Studdy Solution

STEP 1

1. The equation x+2y=9x + 2y = 9 is a linear equation in two variables, xx and yy.
2. To fill in the table, we need to solve for yy given specific values of xx.
3. To graph the equation, we need at least two points that lie on the line defined by the equation.

STEP 2

1. Solve the equation for yy in terms of xx.
2. Verify the table values by substituting xx values and solving for yy.
3. Plot the points on a graph.
4. Draw the line representing the equation.

STEP 3

Solve the equation x+2y=9x + 2y = 9 for yy in terms of xx.
y=9x2 y = \frac{9 - x}{2}

STEP 4

Verify the first table entry (0,4.5)(0, 4.5) by substituting x=0x = 0 into the equation y=9x2y = \frac{9 - x}{2}.
y=902=4.5 y = \frac{9 - 0}{2} = 4.5

STEP 5

Verify the second table entry (9,0)(9, 0) by substituting x=9x = 9 into the equation y=9x2y = \frac{9 - x}{2}.
y=992=0 y = \frac{9 - 9}{2} = 0

STEP 6

Verify the third table entry (5,2)(5, 2) by substituting x=5x = 5 into the equation y=9x2y = \frac{9 - x}{2}.
y=952=2 y = \frac{9 - 5}{2} = 2

STEP 7

Verify the fourth table entry (1,4)(1, 4) by substituting x=1x = 1 into the equation y=9x2y = \frac{9 - x}{2}.
y=912=4 y = \frac{9 - 1}{2} = 4

STEP 8

Plot the first point (0,4.5)(0, 4.5) on the graph.

STEP 9

Plot the second point (9,0)(9, 0) on the graph.

STEP 10

Plot the third point (5,2)(5, 2) on the graph.

STEP 11

Plot the fourth point (1,4)(1, 4) on the graph.

STEP 12

Draw a straight line through the points (0,4.5)(0, 4.5), (9,0)(9, 0), (5,2)(5, 2), and (1,4)(1, 4) to represent the equation x+2y=9x + 2y = 9.
Solution: The table is correctly filled, and the points are plotted on the graph. The line x+2y=9x + 2y = 9 is drawn through these points.

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