SOLUTION: Find the equation, in standard form, of the line that passes through the points (5,6) and (7, 3)

Question 30493: Find the equation, in standard form, of the line that passes through the points (5,6) and (7, 3)
Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
Find the equation, in standard form, of the line that passes through the points (5,6) and (7, 3)
Given two points P(x1,y1) and Q(x2,y2) on a given line
the equation to the given line is
(y-y1)/(y1-y2) = (x-x1)/(x1-x2)----(1)
Therefore given two points P(5,6) and Q(7, 3),
the equation to the line passing through P and Q is
(here x1 = 5, y1 = 6; x2 = 7, y2 = 3 )
(y-6)/(6-3) = (x-5)/(5-7)
That is (y-6)/3 = (x-5)/(-2)
Multiplying by 6 on both the sides (since lcm of 3 and 2 is 6)
2(y-6) = -3(x-5)
2y-12 = -3x+15
3x+2y-12-15 = 0 (grouping like terms,changing sign while changing side)
3x+2y-27 =0 ----(*)
which is the equation to the line in the general form
If by standard form you mean the slope and the y-intercept form
retain the y-term on the left side and take the other terms to the right
and then divide by the coefficient 2 of y
then the slope and y-intercept form of the required line is
y = (-3/2)x +(27/2) ----(**)
Verification: Testing for P(5,6) and Q(7, 3)in (*)
LHS = 3x+2y-27
= 3X(5)+2X(6)-27 (putting x = 5 and y = 6 in (1) )
= 13+12-27
= 27-27
= 0
=RHS
P(5,6) is a point on (*)
Now putting x = 7 and y = 3 in (*)
that is checking if Q(7,3) is a point on (*)
LHS = 3x+2y-27
= 3X(7)+2X(3)-27
= 21+6-27
= 27-27
= 0
=RHS
This implies Q(7,3) is a point on (*)
RELATED QUESTIONS
Find the equation, in standard form, of the line that passes through the points (5,6) and (answered by sdmmadam@yahoo.com)

find the standard form of the equation of the line that passes through the points (9,-3)... (answered by stanbon)

Write the equation in standard form of the line that passes through the points (7,-3) and (answered by josgarithmetic)

Write the equation of a line that passes through the points (3,4) and (-5,-6). In... (answered by Mona27)

Find the equation in slope-intercept form, of the line that passes through the points (3, (answered by checkley75)

find the equation of the line, slope-intercept form, that contains the points: 1. (1,... (answered by josgarithmetic)

Write the relation of the line (equation) that passes through the points (3, -5) and (-1, (answered by josgarithmetic)

Find the equation, in slope-intercept form, of the line that passes through the points... (answered by josmiceli)

Find the equation, in slope-intercept form, of the line that passes through the points... (answered by Mathtut)