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\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
-7 & 0 \\
\hline
0 & 1 \\
\hline
\end{tabular}

What is the slope of the linear function represented in the table?

A. [tex]$-7$[/tex]
B. [tex]$\frac{-1}{7}$[/tex]
C. [tex]$\frac{1}{7}$[/tex]
D. 7

Sagot :

Sure! Let's find the slope of the linear function represented in the given table.

The table provides two coordinates: [tex]\((-7, 0)\)[/tex] and [tex]\((0, 1)\)[/tex].

To find the slope ([tex]\(m\)[/tex]) of a linear function given two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], we use the formula:

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

Let's plug in the coordinates from the table into this formula:

- [tex]\((x_1, y_1) = (-7, 0)\)[/tex]
- [tex]\((x_2, y_2) = (0, 1)\)[/tex]

Now, substitute these values into the slope formula:

[tex]\[ m = \frac{1 - 0}{0 - (-7)} \][/tex]

Simplify the expression in the numerator and the denominator:

[tex]\[ m = \frac{1}{0 + 7} \][/tex]

[tex]\[ m = \frac{1}{7} \][/tex]

Therefore, the slope of the linear function represented in the table is:

[tex]\[ \boxed{\frac{1}{7}} \][/tex]
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