To complete the equation describing how the given points align, we need to determine the linear equation in the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
### Step-by-Step Solution:
1. Identify two points from the table: Let's select the points [tex]\((-4, 21)\)[/tex] and [tex]\((-3, 18)\)[/tex].
2. Calculate the slope (m):
The formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Plugging in [tex]\((x_1, y_1) = (-4, 21)\)[/tex] and [tex]\((x_2, y_2) = (-3, 18)\)[/tex],
[tex]\[
m = \frac{18 - 21}{-3 - (-4)} = \frac{-3}{1} = -3
\][/tex]
3. Determine the y-intercept (b):
Using the equation [tex]\( y = mx + b \)[/tex], we can solve for [tex]\( b \)[/tex]. Let’s use one of the points, say [tex]\((-4, 21)\)[/tex],
[tex]\[
21 = (-3)(-4) + b
\][/tex]
Simplifying this,
[tex]\[
21 = 12 + b \implies b = 21 - 12 = 9
\][/tex]
4. Formulate the linear equation:
With [tex]\( m = -3 \)[/tex] and [tex]\( b = 9 \)[/tex], the equation of the line is:
[tex]\[
y = -3x + 9
\][/tex]
### Conclusion:
The complete equation describing the relationship between [tex]\( x \)[/tex] and [tex]\( y \)[/tex] given the points in the table is:
[tex]\[
y = -3x + 9
\][/tex]
