To determine the slope of the line passing through two points [tex]\( A(0, 1) \)[/tex] and [tex]\( B(1, 5) \)[/tex], we use the formula for the slope [tex]\( m \)[/tex] 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]
For our given points [tex]\( A(0, 1) \)[/tex] and [tex]\( B(1, 5) \)[/tex], we can substitute the coordinates into the formula:
- [tex]\( x_1 = 0 \)[/tex]
- [tex]\( y_1 = 1 \)[/tex]
- [tex]\( x_2 = 1 \)[/tex]
- [tex]\( y_2 = 5 \)[/tex]
Now, plug these values into the slope formula:
[tex]\[
m = \frac{5 - 1}{1 - 0}
\][/tex]
Simplify the numerator:
[tex]\[
5 - 1 = 4
\][/tex]
Simplify the denominator:
[tex]\[
1 - 0 = 1
\][/tex]
So, the slope calculation becomes:
[tex]\[
m = \frac{4}{1} = 4
\][/tex]
Thus, the slope of line [tex]\( AB \)[/tex] is:
[tex]\[
\boxed{4}
\][/tex]
