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]
