Question

Find a and b if the graph ax+2y=b passes through (2,5) and is parallel to 3x-5y=7

i find a= -6/5 b= 38/5

is it correct? thanks

Answer 1

Your answer is correct.

Equations in slope intercept form:

a x + 2 y = b

y = ( - a x + b ) / 2

y = ( - a / 2 ) x + b / 2


3 x - 5 y = 7 -> y = ( - 3 x + 7 ) / - 5

y = ( 3 / 5 ) x - 7 / 5


Parallel lines have the same slope.

( - a / 2 ) = 3 / 5

Cross multiply:

- 5 a = 6

a = - 6 / 5

a x + 2 y = b passes through ( 2 , 5 ) mean x = 2 , y = 5

- ( 6 / 5 ) x + 2 y = b

- ( 6 / 5 ) ∙ 2 + 2 ∙ 5 = b

- 12 / 5 + 10 = b

- 12 / 5 + 50 / 5 = b

38 / 5 = b

b = 38 / 5


a x + 2 y = b

- ( 6 / 5 ) x + 2 y = 38 / 5