To find the slope of the line that passes through the points [tex]\( A(4, 5) \)[/tex] and [tex]\( B(9, 7) \)[/tex], we utilize the slope formula, which is defined as:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here, the coordinates of point [tex]\( A \)[/tex] are [tex]\( (x_1, y_1) = (4, 5) \)[/tex] and the coordinates of point [tex]\( B \)[/tex] are [tex]\( (x_2, y_2) = (9, 7) \)[/tex].
Step-by-Step Calculation:
1. Identify the coordinates:
- Point [tex]\( A \)[/tex]: [tex]\( x_1 = 4 \)[/tex], [tex]\( y_1 = 5 \)[/tex]
- Point [tex]\( B \)[/tex]: [tex]\( x_2 = 9 \)[/tex], [tex]\( y_2 = 7 \)[/tex]
2. Plug the coordinates into the slope formula:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 5}{9 - 4}
\][/tex]
3. Simplify the fraction:
[tex]\[
\text{slope} = \frac{2}{5}
\][/tex]
The slope of the line passing through the points [tex]\( A(4, 5) \)[/tex] and [tex]\( B(9, 7) \)[/tex] is [tex]\( \frac{2}{5} \)[/tex].
The correct answer is:
[tex]\[
\frac{2}{5}
\][/tex]
