Final answer:
The equation of the line with a gradient of 0.5 passing through the point (4, -2) is y = 0.5x - 4, derived using the point-slope form and converting it to the slope-intercept form.
Step-by-step explanation:
The student has asked to work out the equation of a line with a gradient of 0.5 that passes through the point (4, -2). This involves using the point-slope form of a linear equation, which is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Substituting the given point and slope values, we get y + 2 = 0.5(x - 4).
Multiplying through by 2 to clear the fraction, we have 2y + 4 = x - 4, and by arranging the terms, we arrive at the slope-intercept form of the equation, which is y = 0.5x - 4.