Final answer:
To write the equation of a line with a slope of 1/2 that passes through the point (3, -2), the slope-intercept form y = mx + b is used. By substituting the given slope and point into the formula and solving for b, the line equation is determined as y = ½x - 2.25.
Step-by-step explanation:
The question involves finding the equation of a straight line with a known slope and a point it passes through. The slope of the line is given as ½, and the line passes through the point (3, -2). The form that can be used to write the equation of such a line is the slope-intercept form, which is y = mx + b, where 'm' is the slope and 'b' is the y-intercept.
To find the equation of this specific line, first, plug in the slope (m = ½) and the coordinates of the given point (x = 3, y = -2) into the slope-intercept form:
y = mx + b
-2 = (½)(3) + b
-2 = ¼ + b
By subtracting ¼ from both sides, we get:
b = -2 - ¼
b = -2.25
So the equation of the line in slope-intercept form is:
y = ½x - 2.25