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

find the slope of the line through (-2,5) and (4,-7). It's the difference in y coordinates divided by the difference in x coordinates: (5--7)/(-2-4) = (5+7)/-6 = 12/-6=-2

the slope of the perpendicular line is the negative inverse. take -2 =-2/1 and change the sign to +2/1, then flip it upside down to get 1/2 = perpendicular line's slope

y=mx +b is the general formula, with m=slope = 1/2, b is the y intercept. To find b plug in the point (2,9) x=2, y=9

9=(1/2)2 + b

b = 9-1 = 8

y=(1/2)x + 8 is the equation of the perpendicular line through the point (2,9)

It may help to graph it