Q. 3. a. Complete the table with values for x or y that make this equation true:3x+y=15. \begin{tabular}{|c|c|c|c|c|c|c|c|}\hlinex & 2 & 4 & 6 & 0 & 3 & 5 & 37 \\\hliney & 9 & 3 & −3 & 15 & 6 & 0 & 8 \\\hline\end{tabular}b. Create a graph, plot these points, and find the slope of the line that goes through them.\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|}\hline & & & & & & & & & & & & & & \\\hline & & & & & & & & & & & & & & \\\hline & & & & & & & & & & & & & & \\\hline & & & & & & & & & & & & & & \\\hline & & & & & & & & & & & & & & \\\hline & & & & & & & & & & & & & \\\hline & & & & & & & & & & & & & \\\hline\end{tabular}
Substitute x into equation: To find the missing y-values for the given x-values in the equation 3x+y=15, we will solve for y by substituting each x-value into the equation.
Calculate y for x=2: For x=2, we substitute into the equation to get 3(2)+y=15. This simplifies to 6+y=15. Solving for y, we get y=15−6, which is y=9.
Calculate y for x=4: For x=4, we substitute into the equation to get 3(4)+y=15. This simplifies to 12+y=15. Solving for y, we get y=15−12, which is y=3.
Calculate y for x=6: For x=6, we substitute into the equation to get 3(6)+y=15. This simplifies to 18+y=15. Solving for y, we get y=15−18, which is y=−3.
Calculate y for x=0: For x=0, we substitute into the equation to get 3(0)+y=15. This simplifies to 0+y=15. Solving for y, we get y=15.
Calculate y for x=3: For x=3, we substitute into the equation to get 3(3)+y=15. This simplifies to 9+y=15. Solving for y, we get y=15−9, which is y=6.
Calculate y for x=5: For x=5, we substitute into the equation to get 3(5)+y=15. This simplifies to 15+y=15. Solving for y, we get y=15−15, which is y=0.
Calculate y for x=37: For x=37, we substitute into the equation to get 3(37)+y=15. This simplifies to 7+y=15. Solving for y, we get y=15−7, which is y=8.
Plot points on graph: Now that we have all the y-values for the given x-values, we can plot these points on a graph. The points are (2,9), (4,3), (6,−3), (0,15), (3,6), (5,0), and (37,8).
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) and (4,3). The slope m is given by the formula m=x2−x1y2−y1. Substituting the values, we get m=4−23−9=2−6=−3.