Final answer:
The equation for Table 1 is y = 1.5x - 6, and the equation for Table 2 is y = -4x + 6.1. We determine these by calculating the slope and y-intercept from the values in each table.
Step-by-step explanation:
To find the equations of the given systems, we need to determine the slope (m) and y-intercept (b) from each table and write the equations in slope-intercept form (y = mx + b).
For Table 1, we can see that as x increases by 1, y increases by 1.5. So the slope (m) is 1.5. When x is 0, y is -6, which means the y-intercept (b) is -6. Therefore, the equation for Table 1 is y = 1.5x - 6.
For Table 2, as x increases by 1, y decreases by 4.0. Thus, the slope (m) is -4.0. With x at 0, y is 6.1, so the y-intercept (b) is 6.1. Hence, the equation for Table 2 is y = -4x + 6.1.
The equations of the given systems can be found by using the method of substitution. Let's start with table 1. We can use the points (-6, 0), (-4.5, 1), (-3, 2), and (-1.5, 3) to find the equation. Using the formula y = mx + b, where m is the slope and b is the y-intercept, we can find the equation:
y = mx + b
-6 = 0 * m + b
-4.5 = 1 * m + b
-3 = 2 * m + b
-1.5 = 3 * m + b
Solving this system of equations will give us the values of m and b, which will be the equation of the line for table 1. Similarly, we can find the equation for table 2 using the points (6.1, 0), (2.1, 1), (-1.9, 2), and (-5.9, 3). By solving this system of equations, we can find the equation of the line for table 2.