To find the y-intercept of the line that passes through the points (3, 0) and (4, 1), we first need to find the slope of the line.
The slope \( m \) can be calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the coordinates of the points (3, 0) and (4, 1) into the formula:
\[ m = \frac{1 - 0}{4 - 3} = \frac{1}{1} = 1 \]
Now that we have the slope, we can use the point-slope form of the equation of a line, which is given by:
\[ y - y_1 = m(x - x_1) \]
Using the point (3, 0) and the slope \( m = 1 \):
\[ y - 0 = 1(x - 3) \]
This simplifies to:
\[ y = x - 3 \]
To find the y-intercept, we need to evaluate the line equation when \( x = 0 \):
\[ y = 0 - 3 = -3 \]
Thus, the y-intercept of the line is \(-3\).