Question

to represent each linear relationship.
2.

x	3	6	9	12
y	5	-1	-7	-13

m: ____ b: ____
equation: y = _________
to answer each of the following questions.
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Explanation:

Step1: Find the slope \( m \)

We use two points from the table. Let's take \((3, 5)\) and \((6, -1)\) (assuming the \( y \)-values are \( 5, -1, -7, -13 \) with possible typos). The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
\( m=\frac{-1 - 5}{6 - 3}=\frac{-6}{3}=-2 \)

Step2: Find the y - intercept \( b \)

Use the point - slope form \( y - y_1=m(x - x_1) \) with the point \((3,5)\) and \( m = - 2 \).
\( y-5=-2(x - 3) \)
\( y-5=-2x + 6 \)
\( y=-2x+6 + 5 \)
\( y=-2x + 11 \), so \( b = 11 \)

Step3: Write the equation

The slope - intercept form of a linear equation is \( y=mx + b \). Substituting \( m=-2 \) and \( b = 11 \), we get \( y=-2x + 11 \)

Answer:

\( m=-2 \), \( b = 11 \), equation: \( y=-2x + 11 \)