Question

determine if the statement is true or false.

The line 3x-2y=12 is paral;lel to 3x-2y=5, which in turn passes through the point (0, -5/2).

Answer 1

they do have the same slope right? same coefficient for \(x\) and \(y\) namely \(3\) and \(-2\)

Answer 2

if \(x=0\) then \(3x-2y=5\) becomes \(-2y=5\) and so \(y=-\frac{5}{2}\)

Answer 3

3x-2y=12 and 3x-2y=5 are parallel so they have same slope

Answer 4

point slope form of equation 2 is (y-y0)=m(x-x0) ---->(y-y0)=3/2(x-x0).

Answer 5

we have (x0,y0) as (0,-5/2) put this in the point slope form,(y--5/2)=3/2(x-0)

Answer 6

which gives y=3/2x-5/2 which is the second equation

Answer 7

true

Answer 8

still thinking ... hmmm

Answer 9

what has got you confused?

Answer 10

the substituting

Answer 11

ok just put 0 in place of x and -5/2 in place of y

Answer 12

the equation tells about what 'y' will be when 'x' has this value

Answer 13

you want to know if \((0,-\frac{5}{2})\) is on the line

Answer 14

only the points on this line will satisfy that equation

Answer 15

i want to know how'd you get the answer

Answer 16

which means if \(x=0\) then \(y=-\frac{5}{2}\)
replace \(x\) by \(0\) and solve for \(y\)
if you get \(-\frac{5}{2}\) then the answer is "yes"

Answer 17

should i use the point slope form?

Answer 18

\[ 3x-2y=5\] put \(x=0\) and get
\[3\times 0-2y=5\] or \[-2y=5\] divide by \(-2\) and get \[y=-\frac{5}{2}\]

Answer 19

no need for "point slope" here

Answer 20

so you'd just sub it with 0? just like getting the y and x intercept?