Find the equation of the line in intercept form

Question

Find the equation of the line in intercept form that goes through the point (16,-14) and is perpendicular to the equation y=8/5x+5

Answer 1

When lines are perpendicular, the product of their slopes equals -1.

 

So, first, take the opposite sign (-/+) and reciprocal of the slope from the given line:

y = (8/5)x + 5   where 8/5 is slope

 

-5/8 is slope of perpendicular line as (8/5)x(-5/8) = -1

 

Now that we have slope (m), we need a y-intercept (b) by substituting new slope (m) and (x,y) from given point (16,-14) into slope intercept form:

y = mx + b

-14 = (-5/8)(16) + b     (simplify first term on right)

-14 = -10 + b     (add 10 to both sides)

-4 = b     (this is y-intercept)

 

Last, let's put our m (slope) and b (y-intercept) into our equation to give the solution:

 

y = (-5/8)x - 4

Answer 2

The perpendicular slope would be negative reciprocal.  Given the slope m of the first line is (8/5), the slope of a perpendicular line is (-5/8).  Using equation of a line, y-y1=m(x-x1), the equation is

y-(-14) = (-5/8)*(x-16)

y=-5/8X + 10 -14

y = -10 = 10 -14

 

y = -5/8X - 4