find and equation of the line passing through (-3,8) and satisfying the conditions perpendicular to -3x+4y=-23 equation in slope intercept form

Question

how do I do this one this the first time I see the problem. help with the steps please

Answer 1

We need to get the given equation in slope-intercept form.  

 

4y = 3x - 23

 

y = (3/4)x - (23/4)

 

 

Perpendicular lines have negative reciprocal slopes.  Since the slope of the given line is 3/4, the equation of the line we want is

 

 

y = (-4/3)x + b

 

Next, substitute the coordinates into this equation to find b.

 

8 = (-4/3)(-3) + b

 

8 = 4 + b

4 = b

 

 

The equation of the line is

 

y = (-4/3)x + 4