Question

What is the slope of the line parallel to the points (3,-7) and (-6,5)

Answer 1

The slope of the line parallel to the points (3,-7) and (-6,5) is $-\frac{4}{3}$

Solution:

We have been given two points of a line, and we have been asked to find the slope of a line parallel to it.

The given points are: (3,-7) and (-6,5)

According to the definition of parallel lines, two lines in a plane that do not intersect or touch each other at any point are said to be parallel.

And this is only possible if the two lines have the same slope.

Let the slope of the line be denoted by ‘m’.

So, to find the slope of the line given to us we do the following:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$  --- equation 1

Where y and x are coordinates of the points given to us.

Therefore substituting the values eq1 becomes:

$\begin{array}{l}{m=\frac{5-(-7)}{-6-3}} \\\\ {m=\frac{5+7}{-9}=\frac{12}{-9}=-\frac{4}{3}}\end{array}$

Therefore the slope of the line is $-\frac{4}{3}$ So by definition, the slope of a line parallel to this line will also have the slope $-\frac{4}{3}$