Final answer:
To find the equation of the line with slope -1/2 passing through the point (4,1), we substitute the given values into the slope-intercept form y = mx + b and solve for b, resulting in the equation y = (-1/2) x + 3.
Step-by-step explanation:
The question asks us to write the equation of a line with a given slope that passes through a specific point. The slope-intercept form of a line's equation is y = mx + b, where m represents the slope and b is the y-intercept. Given the slope -1/2 and the point (4,1), we can substitute into the slope-intercept form to find b.
Starting with the general form:
y = mx + b
Substituting the given point and slope:
1 = (-1/2) (4) + b
1 = -2 + b
1 + 2 = b
b = 3
So, the equation of the line is:
y = (-1/2) x + 3