Question 201322
Recall that if two lines are perpendicular, then their slopes are the negative reciprocal of each other, that is: {{{m[2] = -1/m[1]}}}
Let's find the slope of the given line:
{{{-8x+5y = 77}}} Solve this equation for y so that you have it in the slope-intercept form: {{{y = mx+b}}}.  Add 8x to both sides.
{{{5y = 8x+77}}} Now divide both sides by 5.
{{{y = (8/5)x + 77/5}}} Compare this with:
{{{y = mx+b}}} and you can see that the slope {{{m[1] = 8/5}}}.
The negative reciprocal of m is:
{{{m[2] = -1/m[1]}}}
{{{m[2] = -(1)/(8/5)}}}
{{{highlight(m[2] = -5/8)}}} so, for the new equation, you can start by writing:
{{{y = (-5/8)x+b}}} To find the value of b, you need to substitute the values of the x- and y-coordinates of the given point (-4, 3) and solve for b.
{{{3 = (-5/8)(-4)+b}}} Simplify.
{{{3 = (5/2)+b}}} Subtract {{{5/2}}} from both sides. Replace({{{3 = 6/2}}})
{{{(6/2)-(5/2) = b}}} or...
{{{b = 1/2}}}  Now you can write the final equation.
{{{highlight(y = (-5/8)x+1/2)}}}