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Given the equation y = 2x − 7 and one point (2, -3), complete the table of values.

Mathematics

ScanSolve AI Answer

Graph of y = 2x − 7

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Key points of y = 2x − 7
Pointxy
y-intercept0−7
x-intercept3.50

Step-by-step solution

2 steps
  1. Step 1: Identify the given equation and points. From the image, the equation appears to be y=2x−7y = 2x - 7. The first point given is (x,y)=(2,−3)(x, y) = (2, -3). Let's verify this point with the equation: y=2(2)−7=4−7=−3y = 2(2) - 7 = 4 - 7 = -3. This matches, so the equation is y=2x−7y = 2x - 7.
  1. Complete the table for the missing values using the equation y=2x−7y = 2x - 7.

    For the second row, x=0x = 0:

    y=2(0)−7y = 2(0) - 7 y=0−7y = 0 - 7 y=−7y = -7

    For the third row, y=0y = 0:

    0=2x−70 = 2x - 7 7=2x7 = 2x x=72x = \frac{7}{2} x=3.5x = 3.5

    For the fourth row, since no value is given, we can choose a simple integer for xx, for example, x=1x = 1:

    y=2(1)−7y = 2(1) - 7 y=2−7y = 2 - 7 y=−5y = -5
  2. Present the completed table.

    The completed table is:

    xy2−30−73.501−5\begin{array}{|c|c|} \hline x & y \\ \hline 2 & -3 \\ \hline 0 & -7 \\ \hline 3.5 & 0 \\ \hline 1 & -5 \\ \hline \end{array}

    The completed table is xy2−30−73.501−5\boxed{\begin{array}{|c|c|} \hline x & y \\ \hline 2 & -3 \\ \hline 0 & -7 \\ \hline 3.5 & 0 \\ \hline 1 & -5 \\ \hline \end{array}}.

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