Answer:
y = (-1/2) x + 4
Explanation:
Given line has slope 2 so the perpendicular line has the slope is -1/2 because ⊥ lines have their slopes negative reciprocal.
Both lines intersect at (4, 2) so this point belongs to both lines.
→general equation of a line y = mx+b where m = slope, b = y-intercept
→the equation for the line that has slope m = -1/2, is y = (-1/2) x+ b ( we do not know b now but will find it)
→we know that the point ( 4, 2) belongs to this line so the equation works for (x= 4, y= 2), substitute those values in the equation y = (-1/2) x+ b
2 = (-1/2)*4+ b which gives us b = 2+ (1/2)*4= 2+ 4/2 = 2+ 2 = 4
The equation of the line that is perpendicular to a line with a slope of 2 and intersects that line at (4,2) is y = (-1/2) x + 4