Question: Fill in the missing numbers to complete the linear equation that gives the rule for this table.
x
y
2 40
3 60
4 80
5 100
y = __x + __
1. **State the problem:** We are given a table of values for $x$ and $y$ and need to find the linear equation of the form $$y = mx + b$$ that fits the data.
2. **Identify the points:** From the table, the points are $(2,40)$, $(3,60)$, $(4,80)$, and $(5,100)$.
3. **Find the slope $m$:** The slope formula is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$
Using points $(2,40)$ and $(3,60)$:
$$m = \frac{60 - 40}{3 - 2} = \frac{20}{1} = 20$$
4. **Write the equation with slope:** So far, $$y = 20x + b$$
5. **Find the y-intercept $b$:** Substitute one point, say $(2,40)$, into the equation:
$$40 = 20 \times 2 + b$$
$$40 = 40 + b$$
Subtract 40 from both sides:
$$40 - 40 = b$$
$$0 = b$$
6. **Final equation:**
$$y = 20x + 0$$
Or simply,
$$y = 20x$$
**Answer:** The missing numbers are $20$ and $0$.