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Chapter 4: Problem 7

Complete the table of values and graph each equation. $$ 2 x=3-y $$ $$ \begin{array}{|c|c|} \hline x & y \\ \hline & 0 \\ \hline 0 & \\ \hline \frac{1}{2} & \\ \hline & 5 \\ \hline \end{array} $$

Short Answer

Expert verified
The completed table of values is: $$ \begin{array}{|c|c|} \hline x & y \\ \hline -1 & 5 \\ \hline 0 & 3 \\ \hline \frac{1}{2} & 2 \\ \hline \frac{3}{2} & 0 \\ \hline \end{array} $$ To graph the equation \(2x = 3 - y\), plot the points (-1, 5), (0, 3), (1/2, 2), and (3/2, 0); then draw a straight line through these points.

Step by step solution

01

(Step 1: Solve the equation for y)

(To find the y-values, we need to solve the given equation for y. The given equation is \(2x = 3 - y\). To solve for y, we will first add y to both sides and then subtract 2x from both sides. Doing so, we have the equation, \(y = 3 - 2x\). Now, we can use this equation to find the missing y-values in the table.)
02

(Step 2: Fill in the table of values)

(Using the equation we found in Step 1, \(y = 3 - 2x\), we can find the missing y-values corresponding to each x-value given in the table. When x is not given, and y = 0: \[0 = 3 - 2x\] \[2x = 3\] \[x = \frac{3}{2}\] When x = 0, and y is not given: \[y = 3 - 2(0)\] \[y = 3\] When x = 1/2, and y is not given: \[y = 3 - 2(\frac{1}{2})\] \[y = 3 - 1\] \[y = 2\] When x is not given, and y = 5: \[5 = 3 - 2x\] \[2x = -2\] \[x = -1\] So, the completed table of values is: $$ \begin{array}{|c|c|} \hline x & y \\ \hline \text{-1} & 5 \\ \hline 0 & 3 \\ \hline \frac{1}{2} & 2 \\ \hline \frac{3}{2} & 0 \\ \hline \end{array} $$ )
03

(Step 3: Graph the equation)

(Now that we have the completed table of values, we can plot the points on a graph. Plot the points: (-1, 5) (0, 3) (1/2, 2) (3/2, 0) Draw a straight line through all the points since this is a linear equation. The graph of the equation \(2x = 3 - y\) is now complete.)

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