Final answer:
The equation of the line that passes through (1,5) with a slope of -\(1/2\) is y = (-\(1/2\))x + \(5.5\) in slope-intercept form.
Step-by-step explanation:
To find an equation of the line that passes through the point (1,5) with a slope of m=-\(1/2\), we can use the point-slope form of a linear equation: y - y1 = m(x - x1). Here, (x1,y1) is the given point through which the line passes, and m is the slope.
Plugging in the given values into the point-slope formula, we get:
y - 5 = (-\(1/2\))(x - 1)
To convert this to the slope-intercept form y = mx + b, we simplify and solve for y:
y - 5 = (-\(1/2\))x + \(1/2\)
Adding 5 to both sides to isolate y, we get:
y = (-\(1/2\))x + \(5.5\)
This is the equation of the line in slope-intercept form, where the slope m indicates the steepness of the line, and b is the y-intercept, which is the point where the line crosses the y-axis.