What is the slope of any line perpendicular to the line passing through $(7,-9)$ and $(-5,-3)$ ?

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Answer 1 · 2018-04-17T10:29:03

$2$
$y = 2x - 23$

If by slope you mean gradient, then first work out the gradient of the line that goes through those points:

$"change in y"/"change in x" = "gradient"$

$((-9) - (-3))/ (7 - (-5)) = (-6) / 12 = -0.5$ (as $(--) = +$ )

The perpendicular gradient will be the negative reciprocal (meaning when multiplied together it produces $-1$ ). This is also known as the 'normal'.

Normal of $-0.5 = 2$

Therefore, gradient is $2$ of the perpendicular line to the line which passes through those 2 points.

If you want the equation of one of those lines then:

$y - (-9) = 2 " x " ( x - 7)$
$y + 9 = 2x - 14$

$y = 2x -23$

What is the slope of any line perpendicular to the line passing through (7,-9)(7,-9) and (-5,-3)(-5,-3)?