Question 154238
(a) The formula is:
{{{(y - y[1]) / (x - x[1]) = (y[2] - y[1]) / (x[2] - x[1])}}}
where
(3, -5) is ({{{x[1]}}},{{{y[1]}}})
(1, -2) is ({{{x[2]}}},{{{y[2]}}})
Actually, you could interchange (3, -5) and (1, -2) and you'd
still get the right answer
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{{{(y - (-5)) / (x - 3) = (-2 - (-5)) / (1 - 3)}}}
{{{(y + 5) / (x - 3) = 3 / (-2)}}}
Multiply both sides by {{{(x - 3)*(-2)}}}
{{{(-2)*(y + 5) = 3*(x - 3)}}}
{{{-2y - 10 = 3x - 9}}}
{{{-2y = 3x + 1}}}
{{{y = -(3/2)x - 1/2}}} answer
check answer:
Does the line pass through (3, -5) and (1, -2)?
{{{-5 = -(3/2)*3 - 1/2}}}
{{{-5 = -(9/2) - 1/2}}}
{{{-5 = -5}}}
OK
{{{-2 = -(3/2)*1 - 1/2}}}
{{{-2 = -2}}}
OK
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(b)The slope of the line perpendicular to this
line must have a slope {{{m[2] = -(1/m[1])}}}
where {{{m[1] = -(3/2)}}}
{{{m[2] = 2/3}}}
It passes through (-1 , -2)
I can use the point-slope formula for this
{{{m = (y - y[1]) / (x - x[1])}}}
{{{2/3 = (y - (-2)) / (x - (-1))}}}
{{{2/3 = (y + 2) / (x + 1)}}}
Multiply both sides by {{{3*(x + 1)}}}
{{{2*(x + 1) = 3*(y + 2)}}}
{{{2x + 2 = 3y + 6}}}
{{{3y = 2x - 4}}}
{{{y = (2/3)x - 4/3}}}
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Does it pass through (-1, -2)?
{{{-2 = (2/3)*(-1) - 4/3}}}
{{{-2 = -(2/3) - 4/3}}}
{{{-2 = -2}}}
OK