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Complete the table of values for a linear function:

[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
$x$ & 4 & -8 & 9 \\
\hline
$y$ & -1 & -2 & \square \\
\hline
\end{tabular}
\][/tex]

Calculate the slope, [tex]\( m \)[/tex]:

[tex]\( m = \)[/tex]



Answer :

GinnyAnswer
To find the slope [tex]\( m \)[/tex] of the linear function given the points (4, -1) and (-8, -2), you can use the formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:

[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

Substituting the coordinates of the points into the formula:

- For the point (4, -1):
- [tex]\( x_1 = 4 \)[/tex]
- [tex]\( y_1 = -1 \)[/tex]
- For the point (-8, -2):
- [tex]\( x_2 = -8 \)[/tex]
- [tex]\( y_2 = -2 \)[/tex]

Now, substitute these values into the slope formula:

[tex]\[ m = \frac{-2 - (-1)}{-8 - 4} = \frac{-2 + 1}{-8 - 4} = \frac{-1}{-12} = \frac{1}{12} \][/tex]

Therefore, the slope [tex]\( m \)[/tex] is:

[tex]\[ m = \frac{1}{12} \approx 0.0833333 \][/tex]

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