Final answer:
The equation of the line perpendicular to 8x + 5y + 4 = 0 and passing through the point (0,2) in slope-intercept form is y = 5/8x + 2.
Step-by-step explanation:
To find the equation of the line perpendicular to the given line, we first need to find the slope of the given line. The equation is in the form of ax + by + c = 0, so we can rewrite it as y = mx + b, where m is the slope. Rearranging the equation, we have y = -8/5x - 4/5. The slope of this line is -8/5. Since the line perpendicular to this has a slope that is the negative reciprocal, the slope of the perpendicular line is 5/8.
Next, we use the point-slope form of a line to find the equation of the perpendicular line. The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line. Substituting the values (0, 2) for (x1, y1) and 5/8 for m, the equation of the line perpendicular to 8x + 5y + 4 = 0 and passing through the point (0, 2) is y - 2 = 5/8(x - 0).
Simplifying the equation, we get y - 2 = 5/8x. To put it in slope-intercept form, we can rearrange the equation as y = 5/8x + 2.