To solve for the slope and the coordinates of a point on the line given the equation [tex]\( y - 4 = \frac{1}{2}(x - 1) \)[/tex], we can follow these steps:
1. Identify the Slope:
- The point-slope form of an equation of a line is written as [tex]\( y - y_1 = m(x - x_1) \)[/tex], where [tex]\( m \)[/tex] is the slope of the line, and [tex]\( (x_1, y_1) \)[/tex] is a point on the line.
- In the given equation [tex]\( y - 4 = \frac{1}{2}(x - 1) \)[/tex], we see that the coefficient of [tex]\( (x - 1) \)[/tex] is [tex]\( \frac{1}{2} \)[/tex].
- Therefore, the slope [tex]\( m \)[/tex] of the line is [tex]\( \frac{1}{2} \)[/tex].
2. Identify a Point on the Line:
- To find a point through which the line passes, we look at the values associated with [tex]\( x \)[/tex] and [tex]\( y \)[/tex] inside parenthesis:
- The term [tex]\( (x - 1) \)[/tex] indicates that the line passes through a point where [tex]\( x = 1 \)[/tex].
- The term [tex]\( (y - 4) \)[/tex] indicates that the line passes through a point where [tex]\( y = 4 \)[/tex].
- Therefore, the point [tex]\( (x_1, y_1) \)[/tex] corresponding to this equation is [tex]\( (1, 4) \)[/tex].
3. Summary:
- The slope of the line is [tex]\( \frac{1}{2} \)[/tex].
- A point on the line is [tex]\( (1, 4) \)[/tex].
Thus, the completed responses would be:
- The slope of the line is [tex]\( \boxed{0.5} \)[/tex]
- A point on the line is [tex]\( \boxed{(1, 4)} \)[/tex]
