Final answer:
To solve the equation y-4=-2(x+3), distribute -2 inside the parenthesis and then add 4 to both sides. The solution is y = -2x - 2. This aligns with understanding how to construct tables and graphs for linear equations like y = 9 + 3x by calculating and plotting points.
Step-by-step explanation:
The student's question requires solving the linear equation y-4=-2(x+3) to find the missing value. To achieve this, we need to perform several algebraic steps:
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- Distribute the -2 across the (x+3) to get y - 4 = -2x - 6.
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- Add 4 to both sides of the equation to isolate y, resulting in y = -2x - 2.
This equation is in the form y = mx + b, where m is the slope and b is the y-intercept. Based on the original line of best fit equation given, y = -173.5 + 4.83x, and the lines Y2 and Y3, which include 2(16.4) as an adjustment to the y-intercept while maintaining the same slope, we can observe how changes in the equation affect the position of the line on a graph.
As for constructing a table and graph for the equation y = 9 + 3x, one would simply choose a series of x-values and calculate the corresponding y-values, as depicted in Table A1 and Figure A1. Plotting these points and connecting them with a line would illustrate the linear relationship between x and y.