Find the standard form of the equation of the line through (3,1) and parallel to the line with equation x-2y = 5.

Answer 1

Greetings! Lets solve this shall we ?

We must find another line parallel to the given line x - 2y = 5. Lets change this equation into slope-intercept form such that

x - 2y = 5............subtract x to both sides

-2y = -x + 5.............Then divide -2 yielding

y = (1/2)x - (5/2)

We must find another line parallel to this line. To do this we need the same slope from the previous equation, the given point (3,1) and the point-slope formula to create this line such that

y - y₁ = m(x - x₁)

y - 1 = (1/2)(x - 3)...........Now distribute the (1/2) inside such that

y - 1 = (1/2)x - (3/2)..... Now add 1 to both sides such that

y = (1/2)x - (1/2)................because -3/2 + 1 = -1/2

I hope this helped!

Answer 2

The given line x - 2y = 5

or x - 5 = 2y

has slope 1/2, since (1/2)x - (5/2) = y

so the parallel line also has slope m=1/2

B = y - mx = 1 - (1/2)(3) = 1 - 3/2 = -1/2

the parallel line has equation y = (1/2)x - 1/2