Question

fill in the missing numbers to complete the linear equation that gives the rule for this table.
x | y
4 | -18
5 | -27
6 | -36
7 | -45
y = \boxed{}x + \boxed{}

Explanation:

Step1: Find the slope (coefficient of x)

We use two points \((x_1,y_1)=(4, - 18)\) and \((x_2,y_2)=(5,-27)\). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-27-(-18)}{5 - 4}=\frac{-9}{1}=-9\). So the coefficient of \(x\) is \(-9\).

Step2: Find the y - intercept (constant term)

Use the point - slope form \(y - y_1=m(x - x_1)\). Substitute \(m=-9\), \(x_1 = 4\), \(y_1=-18\) into it:
\(y-(-18)=-9(x - 4)\)
\(y + 18=-9x+36\)
\(y=-9x + 18\)
We can also verify with another point. For \(x = 6\), \(y=-9\times6+18=-54 + 18=-36\) (which matches the table), and for \(x = 7\), \(y=-9\times7+18=-63 + 18=-45\) (which also matches the table).

Answer:

\(y=-9x + 18\) (So the first box is \(-9\) and the second box is \(18\))