Question

Input the equation of the given line in standard form.

The line through (1, -4) and parallel to 2x + 3y = 4.

Answer 1

do you know how to find the slope in the equation 2x + 3y = 4 ?

Answer 2

put the equation in y = mx + b form, and m will be your slope. Can you find the slope ?

Answer 3

would the slope me 2/3?

Answer 4

be

Answer 5

ok....2x + 3y = 4
3y = -2x + 4
y = -2/3x + 4/3
the slope (the m position) is -2/3
A parallel line will have the same slope.
Now we will use y = mx + b
slope(m) = -2/3
(1,-4) x = 1 and y = -4
now we sub and solve for b
-4 = -2/3(1) + b
-4 = 2/3 + b
-4 - 2/3 = b
-12/3 - 2/3 = b
-14/3 = b
your parallel equation is : y = -2/3x - 14/3, but we need it in standard form
Ax + By = C

y = -2/3x - 14/3 -- multiply by 3
3y = -2x - 14 -- add 2x to both sides
2x + 3y = -14 ====> standard form

any questions ?

Answer 6

No. Thank you so much! :)

Answer 7

wait...I think I messed up...hold on

Answer 8

-4 = -2/3(1) + b
-4 = -2/3 + b
-4 + 2/3 = b
-12/3 + 2/3 = b
-10/3 = b

y = -2/3x - 10/3 -- multiply by 3
3y = -2x - 10 -- add 2x
2x + 3y = -10 --->standard form

sorry about that

Answer 9

thats better :)