Questions: Construct a table of solutions and then graph the equation. y=9x-3

Construct a table of solutions and then graph the equation. y=9x-3
Transcript text: Construct a table of solutions and then graph the equation. \[ y=9 x-3 \]
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Solution

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Solution Steps

Step 1: Choose values for x

Select a few values for \( x \) to construct a table of solutions. Common choices are \( x = -1, 0, 1 \).

Step 2: Calculate corresponding y values

Use the equation \( y = 9x - 3 \) to find the corresponding \( y \) values for each chosen \( x \).

  • For \( x = -1 \): \[ y = 9(-1) - 3 = -9 - 3 = -12 \]

  • For \( x = 0 \): \[ y = 9(0) - 3 = 0 - 3 = -3 \]

  • For \( x = 1 \): \[ y = 9(1) - 3 = 9 - 3 = 6 \]

Step 3: Construct the table of solutions

Create a table with the calculated values.

\[ \begin{array}{c|c} x & y \\ \hline -1 & -12 \\ 0 & -3 \\ 1 & 6 \\ \end{array} \]

Step 4: Plot the points on the graph

Plot the points \((-1, -12)\), \((0, -3)\), and \((1, 6)\) on the provided graph.

Step 5: Draw the line

Connect the plotted points with a straight line to represent the equation \( y = 9x - 3 \).

Final Answer

The table of solutions is: \[ \begin{array}{c|c} x & y \\ \hline -1 & -12 \\ 0 & -3 \\ 1 & 6 \\ \end{array} \]

The graph of the equation \( y = 9x - 3 \) is a straight line passing through the points \((-1, -12)\), \((0, -3)\), and \((1, 6)\).

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