Answer:
To find the value of ( r ), we can use the slope formula ( m = \frac{y_2 - y_1}{x_2 - x_1} ), where ( m ) is the slope and ( (x_1, y_1) ) and ( (x_2, y_2) ) are the coordinates of the two points.
Given the slope ( m = 2 ) and the points ( (r, 3) ) and ( (5, 9) ), we can plug these into the slope formula:
[ 2 = \frac{9 - 3}{5 - r} ]
Solving for ( r ):
[ 2 = \frac{6}{5 - r} ]
[ 2(5 - r) = 6 ]
[ 10 - 2r = 6 ]
[ 10 - 6 = 2r ]
[ 4 = 2r ]
[ r = 2 ]
So, the value of ( r ) that makes the line passing through ( (r, 3) ) and ( (5, 9) ) have a slope of 2 is ( r = 2 ).
