Question

A line passes through A(3,7) and B(-4,9) find the value of a if C (a 1) is on the line

Answer 1

What we need to do first, is to write the equation of the line through points A and B.


the slope of the line through A(3, 7) and B(-4, 9) is


`m= (9-7)/(-4-3)= (2)/(-7)=- (2)/(7)`


the equation of the line is :


`y-7=- (2)/(7)(x-3)\\\\y-7=- (2)/(7)x+ (6)/(7)\\\\y= - (2)/(7)x+ (6)/(7)+ (49)/(7)\\\\y= - (2)/(7)x+ (55)/(7)`


C(a, 1) is on this line so it must satisfy the equation:


`y= - (2)/(7)x+ (55)/(7) \\\\1= - (2)/(7)a+ (55)/(7)\\\\ (2)/(7)a= (48)/(7)\\\\2a=48\\\\a=24`