Question

A line passes through the two points (-4,6) and (2,-5). Calculate the following parts:

Answer 1

A line passes through the two points (-4,6) and (2,-5). 11x +6y - 80 = 0 is the given line equation.

What is the slope of a line which passes through points ( p,q) and (x,y)?

Its slope would be:

$m = \dfrac{y-q}{x-p}$

The slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.

The slope m of the line is given as

$m = \dfrac{y-q}{x-p}\\\\ m = \dfrac{-5-6}{2+4}\\\\ m = \dfrac{-11}{6}$

The equation of a line is  

$( y -y_0) = m (x - x_0)\\\\( y -6) = \dfrac{-11}{6} (x+4)\\\\6( y -6) = (-11) (x+4)\\\\6y -36 = (-11x +44)\\\\11x +6y - 80 = 0$

Hence, the equation is  11x +6y - 80 = 0

Learn more about slopes here:

brainly.com/question/2503591

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