Question

What is the equation of the line passing through `(3,9)` and `(1,2)`?

Answer 1

To find the equation of a line passing through the points
`( 3, 9 )` and `(1, 2)`, we must first determine the slope of the line. Using the slope formula, the slope of the line is,

#m = ( y2 - y1 ) / ( x2 - x1 )=> m = ( 2- (9 ) ) / ( 1 - 3 )=> m = ( -7) / ( -2 )=> m = 7/2 #
Now, we simply plug in the value of the slope and the x and y values of either point into the point-slope equation.
#y -9 = m ( x - 3 )=> y - ( 9 ) = ( 7/2 )( x - 3 )=> y -9 = ( 7/2 )( x - 3 )#

Hence, the equation of the line is,
`y -9 = ( 7/2 )( x - 3 )`