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 

$m= \frac{9-7}{-4-3}= \frac{2}{-7}=- \frac{2}{7}$


the equation of the line is :

$y-7=- \frac{2}{7}(x-3)\\\\y-7=- \frac{2}{7}x+ \frac{6}{7}\\\\y= - \frac{2}{7}x+ \frac{6}{7}+ \frac{49}{7}\\\\y= - \frac{2}{7}x+ \frac{55}{7}$


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

$y= - \frac{2}{7}x+ \frac{55}{7} \\\\1= - \frac{2}{7}a+ \frac{55}{7}\\\\ \frac{2}{7}a= \frac{48}{7}\\\\2a=48\\\\a=24$