To fill in the missing values in the table, we can substitute the given equation y + 4 = 3x with the corresponding values of x.
Let's start with the missing x-value in the first row. Looking at the equation, we have y + 4 = 3x.
To solve for x, we need to isolate it. Subtract 4 from both sides of the equation:
y + 4 - 4 = 3x - 4
y = 3x - 4
Now, we can use this equation to find the missing x-value in the first row, where y = -7:
-7 = 3x - 4
To isolate x, add 4 to both sides of the equation:
-7 + 4 = 3x - 4 + 4
-3 = 3x
Divide both sides of the equation by 3:
-3/3 = (3x)/3
-1 = x
So the missing x-value in the first row is -1. Now let's move on to the missing y-value in the second row.
We can use the same equation, y = 3x - 4, to find the missing y-value when x = 0:
y = 3(0) - 4
y = -4
So the missing y-value in the second row is -4.
Next, let's find the missing x-value in the second row when y = 8:
8 = 3x - 4
8 + 4 = 3x
12 = 3x
x = 4
Finally, let's use the equation to find the missing y-value in the last row when x = -34:
y = 3(-34) - 4
y = -102 - 4
y = -106
So the missing y-value in the last row is -106.
Now the table should be filled as follows:
X -7 -1 0 4
Y -7 8 -4 -106