Question

a linear relationship is shown in the table.

x	-4	-3	-2	-1
y	16.3	13.3	10.3	7.3

which of the following equations models the relationship?

1. $y + 1 = 3(x + 7.3)$
2. $y - 1 = 3(x - 7.3)$
3. $y + 7.3 = -3(x - 1)$
4. $y - 7.3 = -3(x + 1)$

Explanation:

Step1: Calculate the slope

To find the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let's take two points from the table, say \((-4, 16.3)\) and \((-3, 13.3)\).
\[
m=\frac{13.3 - 16.3}{-3 - (-4)}=\frac{-3}{1}=- 3
\]

Step2: Use point - slope form

The point - slope form of a linear equation is \( y - y_1=m(x - x_1) \), where \((x_1,y_1)\) is a point on the line and \( m \) is the slope. Let's use the point \((-1,7.3)\) (from the table when \( x=-1,y = 7.3\)) and \( m=-3 \).
Substitute \( x_1=-1,y_1 = 7.3\) and \( m=-3\) into the point - slope form:
\[
y - 7.3=-3(x-(-1))
\]
Simplify the equation:
\[
y - 7.3=-3(x + 1)
\]

Answer:

\( y - 7.3=-3(x + 1) \)