Question

write the slope intercept form of the equation of the line described
through (-4,-5) perpendicular to y=-2x+5
steps please but not too long though

Answer 1

since the slope of y=-2x+5 is -2, you want a line with slope = 1/2
so start with the point-slope form:
y+5 = 1/2 (x+4)
now just rearrange as desired

Answer 2

perpendicular lines have slopes which are negative-reciprocals

-2 ---> 1/2

using point-slope ... y + 5 = 1/2 (x + 4)

solving for y ... y = 1/2 x - 3

Answer 3

Perpendicular lines have slopes which are negative reciprocals.

In this case:

y = - 2 x + 5

Slope of this line is - 2

Slope of perpendicular line is negative reciprocals :

m = – 1 / ( - 2 ) = 1 / 2

Slope-Intercept form of a straight line :

y = m x + b

y = 1 / 2 x + b

Put x = - 4 , y = - 5 in this equation

- 5 = ( 1 / 2 ) • ( - 4 ) + b

- 5 = - 2 + b

Add 2 to both sides

- 3 = b

b = - 3

So equation of your perpendicular line:

y = 1 / 2 x + b

y = 1 / 2 x - 3