Question: Fill in the missing numbers to complete the linear equation that gives the rule for this table.
x y
0 55
1 40
2 25
3 10
1. **State the problem:** We are given a table of values for $x$ and $y$ and need to find the linear equation rule that relates $x$ and $y$.
2. **Identify the points:** The points from the table are $(0, 55)$, $(1, 40)$, $(2, 25)$, and $(3, 10)$.
3. **Recall the linear equation form:** A linear equation can be written as $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept.
4. **Calculate the slope $m$:** The slope is the change in $y$ divided by the change in $x$ between any two points.
Using points $(0, 55)$ and $(1, 40)$:
$$m = \frac{40 - 55}{1 - 0} = \frac{-15}{1} = -15$$
5. **Find the y-intercept $b$:** The y-intercept is the value of $y$ when $x=0$.
From the table, when $x=0$, $y=55$, so:
$$b = 55$$
6. **Write the equation:** Substitute $m = -15$ and $b = 55$ into the linear equation:
$$y = -15x + 55$$
7. **Verify with other points:** Check if the equation fits other points.
For $x=2$:
$$y = -15(2) + 55 = -30 + 55 = 25$$ which matches the table.
For $x=3$:
$$y = -15(3) + 55 = -45 + 55 = 10$$ which also matches.
**Final answer:** The linear equation rule for the table is:
$$y = -15x + 55$$