To find the slope of a line passing through two points $A(x_1, y_1)$ and $B(x_2, y_2)$, we use the formula:

$\text{slope} = m = \frac{y_2 - y_1}{x_2 - x_1}$

Given the points $A(4, 5)$ and $B(9, 7)$:

• $x_1 = 4$, $y_1 = 5$
• $x_2 = 9$, $y_2 = 7$

Substitute these values into the slope formula:

$m = \frac{7 - 5}{9 - 4} = \frac{2}{5}$

Therefore, the slope of line $AB$ is $\frac{2}{5}$.

Would you like more details on this solution or have any other questions?

Here are 5 related questions to expand your understanding:

1. How do you determine the slope if one of the points is at the origin?
2. What is the slope of a vertical line?
3. How do you find the slope-intercept form of the line using its slope and one point?
4. What is the relationship between the slopes of two perpendicular lines?
5. How can the slope be used to determine if two lines are parallel?

Tip: Remember, the slope represents the rate of change between the $y$ and $x$ values of two points on a line.