Question 675290
Find an equation of the line that is perpendicular to y=-7/5x+10 and passes through (2,1). write in slope intercept form.

Solution:

Given line         
y = -7/5x  + 10

or

7/5x + y -10 = 0

Slope of given line

m1 = -coefficient of x / coefficient of y

coefficien of x = 7/5, coefficient of y = 1

so

m1 = -7/5

since the required line is perpendicular of the given line.

then the slope of required line will be

m2 = -1/m1

i.e.

m2 = -1/-7/5

or

m2 = 5/7

since the line passes through (2, 1) = (x1, y1)

therefore the required line will be

y - y1 = m2(x - x1)

or

y - 1 = 5/7(x - 2)

or

y - 1 = 5/7x - 10/7

or

y = 5/7x - 10/7 + 1

or

y = 5/7x - 3/7

This is the required equation of the perpendicular line passes through (2, 1)
in slope-intercept form (y = mx + b).