Question 82844
If you have a point and you know the slope, then you have all you need to write the equation of a line.
The point is given.
Whats the slope?
I know that to find a perpendicular to any given line, the slope of
that perpendicular will be {{{m[p] = -(1/m)}}} where m is the slope
of the given line.
So our line has a line intersecting it which is {{{4x - 5y = 7}}}
Put it in the form {{{y = mx + b}}} where m is the slope
{{{4x - 5y = 7}}}
{{{-5y = -4x + 7}}}
{{{5y = 4x - 7}}}
{{{y = (4/5)x - 7/5}}}
{{{m[p] = 4/5}}}
Go back to {{{m[p] = -(1/m)}}} and find m of the unknown line
{{{4/5 = -(1/m)}}}
{{{1/m = -(4/5)}}}
{{{1 = -(4/5)m}}}
{{{m = -(5/4)}}}
So the unknown line goes through (2,6) and has a slope {{{-(5/4)}}}
Use the point-slope formula which is
{{{m = (y - y[1]) / (x - x[1])}}}
{{{-(5/4) = (y - 6) / (x - 2)}}}
{{{-(5/4)*(x - 2) = y - 6}}}
{{{-(5/4)x + 5/2 = y - 6}}}
{{{-5x + 10 = 4y - 24}}}
{{{4y = -5x + 34}}}
{{{y = -(5/4)x + 17/2}}} answer
Is the slope {{{-(5/4)}}}? yes
Does it contain the point (2,6)? Find out
{{{y = -(5/4)x + 17/2}}}
{{{6 = -(5/4)*2 + 17/2}}}
{{{6 = -(5/2) + 17/2}}}
{{{12 = -5 + 17}}}
{{{12 = 12}}} yes
The answer must be right