To find the slope of the line between points [tex]\(A\)[/tex] and [tex]\(B\)[/tex], we need to use the formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Given the coordinates:
- Point [tex]\(A\)[/tex] has coordinates [tex]\((400, 40)\)[/tex], where [tex]\(x_1 = 400\)[/tex] and [tex]\(y_1 = 40\)[/tex].
- Point [tex]\(B\)[/tex] has coordinates [tex]\((480, 60)\)[/tex], where [tex]\(x_2 = 480\)[/tex] and [tex]\(y_2 = 60\)[/tex].
Now, let's plug these coordinates into the slope formula:
[tex]\[
\text{slope} = \frac{60 - 40}{480 - 400}
\][/tex]
First, calculate the differences in the numerator and the denominator:
[tex]\[
y_2 - y_1 = 60 - 40 = 20
\][/tex]
[tex]\[
x_2 - x_1 = 480 - 400 = 80
\][/tex]
Now, divide the difference in the [tex]\(Y\)[/tex]-coordinates by the difference in the [tex]\(X\)[/tex]-coordinates:
[tex]\[
\text{slope} = \frac{20}{80} = 0.25
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{+0.25}
\][/tex]
So, the slope of the line between points [tex]\(A\)[/tex] and [tex]\(B\)[/tex] is [tex]\(\boxed{+0.25}\)[/tex].
