Question 83770
1)
Remember that parallel lines have identical slopes.
The first thing you ought to do is put your equations into the slope-intercept form:
y = mx + b where m is the slope and b is the y-intercept.
{{{-7x+8y = 13}}} Add 7x to both sides.
{{{8y = 7x+13}}} Now divide both sides by 8.
{{{y = (7/8)x+13/8}}} Here, you can see that the slope, {{{m = 7/8}}}
{{{Ax+4y = 15}}}Subtract Ax from both sides.
{{{4y = -Ax+15}}} Now divide both sides by 4.
{{{y = (-A/4)x+15/4}}} Here, you can see that the slope,{{{m = -A/4}}}
So, if you set these two slope equal to each other, you can solve for A.
{{{-A/4 = 7/8}}} Multiply both sides by -4.
{{{A = (7/8)(-4)}}}
{{{A = -7/2}}}
2)
Remember that perpendicular lines have slopes that are the negative reciprocal of each other.
{{{20x+5y = 18}}} Subtract 20x from both sides.
{{{5y = -20x+18}}} Now divide both sides by 5.
{{{y = -4x+18/5}}} Here, the slope is {{{m = -4}}}
{{{Ax+17y = 9}}} Subtract Ax from both sides.
{{{17y = -Ax+9}}} Now divide both sides by 17.
{{{y = (-A/17)x+9/17}}} Here, the slope,{{{m = -A/17}}}
Now you want to set one of the slopes equal to the negative reciprocal of the other.
{{{-A/17 = -(1/-4)}}} Simplify and solve for A. Multiply both sides by -17.
{{{A = (1/4)(-17)}}}
{{{A = -17/4}}}