Question

Find the equation of the line through the point P (-5, 1) and parallel to

the line joining the points A (7, -1) and B (0, 3)​

Answer 1

The equation of the line through the point P (-5, 1) and parallel to the line joining the points A (7, -1) and B (0, 3)​ is 7y + 4x  = -13.

Here, according to the given information, we are given that,

A line joins the points that are A (7, -1) and B (0, 3)​.

Now, in order to find the line parallel to this given line, we first need to find the slope of the given line to proceed with the calculations.

Now, the slope of the line joining the points that are A (7, -1) and B (0, 3)​ is equal to $\frac{3 + 1}{0-7}$.

This is equal to $\frac{-4}{7}$.

Now, in order to find the equation of the line through the point P (-5, 1) and parallel to the given line,

We know that, $( y_{2} -y_{1} ) = m( x_{2} -x_{1} )$

Here, m is the slope of the given line.

Then, we get,

(y - 1) = $\frac{-4}{7}$ (x + 5)

Or, 7y - 7 = -4x - 20

Or, 7y + 4x  = -13

Hence, the equation of the line through the point P (-5, 1) and parallel to

the line joining the points A (7, -1) and B (0, 3)​ is 7y + 4x  = -13.

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