Question

a straight line passes through the point p(2,-5) and q(4,3).find the value of P,if PQ passes through the point (p-1,p+4).

Answer 1

I hope it will help you :-)

Answer 2

The value of P is 7.

Given:

A straight line passes through two points, p(2,-5) and q(4,3)

Line PQ passes through the point (p-1,p+4)

To find:

The value of P.

Solution:

Given points through which the straight line passes are p(2,-5) and q(4,3).

There is a proper formula to find the equation of the line passing through two points.

Another method is by finding the slope.

The slope(m) of the two given points is 4.

Using slope and any of the given points we can find the equation of the straight line.

y=mx+c,..... equation 1

here ( x,y) is the arbitrary point, m is the slope and c is the constant.

To find the value of the constant put any point in equation 1

taking the point p(2,-5)

-5=4(2)+c

c= -13

Putting the value of c and with point q in equation 1;

The equation of the straight line passing through p and q is y=4x-13..... equation 2

To find the value of (p-1,p+4) put it in equation 2 because PQ passes through the point and so, will satisfy the equation.

P+4=4(P-1)-13[ by equation 2]

P+4=4P-4-13

4+17=3P

3P=21

P=7.

Hence, The value of P is 7.