Explanation:
To find the equation of a line perpendicular to -2x+y= 9, we first need to determine the slope of the given line. We can rewrite -2x+y= 9 in slope-intercept form (y=mx+b) by isolating y:
-2x+y=9
y=2x+9
So the slope of the given line is 2. The slope of any line perpendicular to this line will be the negative reciprocal of this slope, which is -1/2.
Next, we can use the point-slope form of the equation of a line to find the equation of the line that passes through the point (6, 2) with a slope of -1/2:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the given point. Plugging in the values, we get:
y - 2 = (-1/2)(x - 6)
Simplifying this equation, we get:
y - 2 = (-1/2)x + 3
y = (-1/2)x + 5
So the equation of the line perpendicular to -2x+y= 9 that passes through the point (6, 2) is y = (-1/2)x + 5.