To determine the slope of the line that passes through the points [tex]\((0, 5)\)[/tex] and [tex]\((10, 0)\)[/tex], we use the formula for the slope of a line that passes through two points:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here, the points given are:
[tex]\((x_1, y_1) = (0, 5)\)[/tex] and [tex]\((x_2, y_2) = (10, 0)\)[/tex].
We substitute these coordinates into the slope formula:
[tex]\[
\text{slope} = \frac{0 - 5}{10 - 0}
\][/tex]
Calculating the numerator and the denominator separately, we get:
[tex]\[
0 - 5 = -5 \quad \text{and} \quad 10 - 0 = 10
\][/tex]
So, the expression for the slope becomes:
[tex]\[
\text{slope} = \frac{-5}{10}
\][/tex]
Simplifying the fraction:
[tex]\[
\frac{-5}{10} = -0.5
\][/tex]
Hence, the slope of the line that passes through the points [tex]\((0, 5)\)[/tex] and [tex]\((10, 0)\)[/tex] is [tex]\(-0.5\)[/tex].
