i do not know how to solve this

Question

Line ℓ passes through (-2, 5) and (4, -7). Write an equation for the line that passes through (2, 9) and is perpendicular

to line ℓ. Leave in slope-intercept form.

Answer 1

line through (-2,5) and (4,-7) has slope = (5+7)/(-2-4)=12/-6 = -2

a perpendicular line has the negative inverse of -2 = 1/2

the perpendicular line through (2,9)

is

y=x/2 +b

9=2/2+b

b =9-1=8

y=x/2 +8 is that perpendicular line through the given point in slope intercept form

or

y = .5x+8 with slope= .5, intercept=8