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a. Complete the table with values for 
x or 
y that make this equation true:


3x+y=15". "





x
2
4
6
0
3
5

(7)/(3)



y
9
3
-3
15
6
0
8




b. Create a graph, plot these points, and find the slope of the line that goes through them.

33. a. Complete the table with values for x x or y y that make this equation true:\newline3x+y=15 3 x+y=15 \text {. } \newline\begin{tabular}{|c|c|c|c|c|c|c|c|}\newline\hlinex x & 22 & 44 & 66 & 00 & 33 & 55 & 73 \frac{7}{3} \\\newline\hliney y & 99 & 33 & 3-3 & 1515 & 66 & 00 & 88 \\\newline\hline\newline\end{tabular}\newlineb. Create a graph, plot these points, and find the slope of the line that goes through them.\newline\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|}\newline\hline & & & & & & & & & & & & & & \\\newline\hline & & & & & & & & & & & & & & \\\newline\hline & & & & & & & & & & & & & & \\\newline\hline & & & & & & & & & & & & & & \\\newline\hline & & & & & & & & & & & & & & \\\newline\hline & & & & & & & & & & & & & \\\newline\hline & & & & & & & & & & & & & \\\newline\hline\newline\end{tabular}

Full solution

Q. 33. a. Complete the table with values for x x or y y that make this equation true:\newline3x+y=15 3 x+y=15 \text {. } \newline\begin{tabular}{|c|c|c|c|c|c|c|c|}\newline\hlinex x & 22 & 44 & 66 & 00 & 33 & 55 & 73 \frac{7}{3} \\\newline\hliney y & 99 & 33 & 3-3 & 1515 & 66 & 00 & 88 \\\newline\hline\newline\end{tabular}\newlineb. Create a graph, plot these points, and find the slope of the line that goes through them.\newline\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|}\newline\hline & & & & & & & & & & & & & & \\\newline\hline & & & & & & & & & & & & & & \\\newline\hline & & & & & & & & & & & & & & \\\newline\hline & & & & & & & & & & & & & & \\\newline\hline & & & & & & & & & & & & & & \\\newline\hline & & & & & & & & & & & & & \\\newline\hline & & & & & & & & & & & & & \\\newline\hline\newline\end{tabular}
  1. Substitute xx into equation: To find the missing yy-values for the given xx-values in the equation 3x+y=153x + y = 15, we will solve for yy by substituting each xx-value into the equation.
  2. Calculate yy for x=2x=2: For x=2x = 2, we substitute into the equation to get 3(2)+y=153(2) + y = 15. This simplifies to 6+y=156 + y = 15. Solving for yy, we get y=156y = 15 - 6, which is y=9y = 9.
  3. Calculate yy for x=4x=4: For x=4x = 4, we substitute into the equation to get 3(4)+y=153(4) + y = 15. This simplifies to 12+y=1512 + y = 15. Solving for yy, we get y=1512y = 15 - 12, which is y=3y = 3.
  4. Calculate yy for x=6x=6: For x=6x = 6, we substitute into the equation to get 3(6)+y=153(6) + y = 15. This simplifies to 18+y=1518 + y = 15. Solving for yy, we get y=1518y = 15 - 18, which is y=3y = -3.
  5. Calculate yy for x=0x=0: For x=0x = 0, we substitute into the equation to get 3(0)+y=153(0) + y = 15. This simplifies to 0+y=150 + y = 15. Solving for yy, we get y=15y = 15.
  6. Calculate yy for x=3x=3: For x=3x = 3, we substitute into the equation to get 3(3)+y=153(3) + y = 15. This simplifies to 9+y=159 + y = 15. Solving for yy, we get y=159y = 15 - 9, which is y=6y = 6.
  7. Calculate yy for x=5x=5: For x=5x = 5, we substitute into the equation to get 3(5)+y=153(5) + y = 15. This simplifies to 15+y=1515 + y = 15. Solving for yy, we get y=1515y = 15 - 15, which is y=0y = 0.
  8. Calculate yy for x=73x=\frac{7}{3}: For x=73x = \frac{7}{3}, we substitute into the equation to get 3(73)+y=153\left(\frac{7}{3}\right) + y = 15. This simplifies to 7+y=157 + y = 15. Solving for yy, we get y=157y = 15 - 7, which is y=8y = 8.
  9. Plot points on graph: Now that we have all the yy-values for the given xx-values, we can plot these points on a graph. The points are (2,9)(2, 9), (4,3)(4, 3), (6,3)(6, -3), (0,15)(0, 15), (3,6)(3, 6), (5,0)(5, 0), and (73,8)(\frac{7}{3}, 8).
  10. Find slope of line: To find the slope of the line, we can use any two points from the table. Let's use (2,9)(2, 9) and (4,3)(4, 3). The slope mm is given by the formula m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}. Substituting the values, we get m=3942=62=3m = \frac{3 - 9}{4 - 2} = \frac{-6}{2} = -3.

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