Question

Find the equation of the line passing through the point P(4, -5) and parallel to the line joining the points A(3, 7) and B(-2, 4).​

Answer 1

Answer:

The equation is : 3x-5y-37=0

Answer 2

Given ,

A line passing through the point P(4,-5) and parallel to the line joining the points A(3,7) and B(-2,4)

We know that , the slope of the line is given by

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

Thus ,

m = (4 - 7)/(-2 - 3)

m = -3/-5

m = 3/5

Now , if two lines are parallel to each other then their slopes are equal

Therefore ,

• The slope of the line passing through P(4, -5) is 3/5

Thus , the equation of the line will be

3/5 = (y - (-5))/(x - 4))

3x - 12 = 5y + 25

3x - 5y + 37 = 0

Therefore ,

• The required equation of the line is 3x - 5y + 37 = 0