Question 82844
Write the equation of the line that satisfies the given condition: contains the point (2,6) and is perpendicular to the line 4x-5y=7.
First, put the equation in slope intercept form:{{{highlight(y=mx+b)}}}, where m=slope and b=y-intercept.
{{{4x-5y=7}}}
{{{-4x+4x-5y=-4x+7}}}
{{{-5y=-4x+7}}}
{{{-5y/-5y=(-4/-5)x-7/5}}}
{{{y=(4/5)x-7/5}}}
{{{y=highlight(4/5)x-7/5}}}  The slope of their line is 4/5.
Perpendicular lines have slopes that are negative reciprocals of each other, so our slope, m=-5/4
We can use the point slope formula to find the equation of our line: {{{highlight(y-y[1]=m(x-x[1]))}}}, m=slope and (x1,y1) is the given point.
m=-5/4 x1=2 and y1=6
{{{y-6=(-5/4)(x-2)}}}
{{{4(y-6)=4(-5/4)(x-2)}}}
{{{4y-24=-5(x-2)}}}
{{{4y-24=-5x+10}}}
{{{4y-24+24=-5x+10+24}}}
{{{4y=-5x+34}}}
{{{5x+4y=5x-5x+34}}}
{{{5x+4y=34}}}
Happy Calculating!!!!