# ``passes through `(2, 1)`, parallel to graph `2x + 3y = 6` Graph the line that satisfies each set of conditions.

*print*Print*list*Cite

Student Comments

kspcr111 | Student

Given the line passes through (2, 1), parallel to graph of `2x+3y =6`

as the slope of the line `2x+3y =6` is as follows

`2x+3y =6`

=> `3y = -2x+6`

=> `y = (-2/3) x +(6/3)`

=> `y=(-2/3) x +2`

this is of the form `y= mx +c` where m is the slope

so the slope of the line `2x+3y =6` is `m =` ` -2/3`

so the line passing through the point `(x,y)=(2,1)` is also -2/3 as both the lines are parallel

then the line equation passing through` (2,1)` is follows

`y= mx+c`

`1 = (-2/3)*2+c`

`1= -4/3 +c`

`c = 1+4/3 = 7/3`

so the desired equation of the line is

`y = (-2/3)x + 7/3`

and it is plotted and in the attachments and the point `(2,1)` is plotted with a blue dot