Question 741281
Find the slope intercept equation of the line: perpendicular to 4x+5y=3 and pass through (0,5)
:
Find the slope of the given equation first, put in the slope intercept form
4x + 5y = 3
 put in the slope intercept form (y = mx + b)
5y = -4x + 3
divide eq by 5
y = {{{-4/5}}}x + {{{3/5}}}
Slope m1 = {{{-4/5}}}
:
The relationship of the slopes of perpendicular lines can be written:
m1 * m2 = -1
{{{-4/5}}} * m2 = -1
find m2, the slope of the perpendicular line
m2 = -1 * {{{-5/4}}}
m2 = {{{5/4}}}
:
Use the point/slope form to find the equation y - y1 - m(x - x1)
where
m = = {{{5/4}}}
x1 = 0
y1 = 5
y - 5 = {{{5/4}}}(x - 0)
y = {{{5/4}}}x + 5; the equation of the perpendicular line
:
Lots like this
{{{ graph( 400, 400, -10, 8, -6, 10, -.8x+3, 1.25x+5) }}}