What is the value of p if the line x + py + 6 = 0, passes through the point (3, 1)?  

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given the line x + py + 6 = 0

Given the point (3,1) passes through the line.

Then, the point should verify the equation of the line.

==> Let us substitute the point ( 3,1) into the equation of the line.

==> x + py + 6 = 0

==> 3 + 1*p + 6 = 0

==> 3 + p + 6 = 0

==> p+ 9 = 0

==> Now we will subtract 9 from both sides.

==> p= -9

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The line x + py + 6 = 0 passes through the point (3, 1). So we replace the values of the coordinates of the points in the equation of the line.

x + py + 6 = 0

=> 3 + 1*p + 6 = 0

=> p + 9 = 0

=> p = -9

Therefore the required value of p is -9.

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

To find p if  x + py + 6 = 0, passes through the point (3, 1).

If a line ax+by+c passes through the point (1,y1), then the coordinates should satisfy the line ax+y+c = 0:

=> ax1+by1+c = 0.

Therefore since the lines x+py+6 = 0 passes through (3,1), the coordinates (3, 1) should satisfy the equation of the line x+py+6 = 0.

=> 3+p*1 +6 = 0.

=> p = -3-6 = -9.

=> p = -9.

Therefore the value of p = -9. And the line x-9y+6 should pass through (3,1).

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