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

Textbook Question

Chapter 2, 2.3 - Problem 47 - Glencoe Algebra 2 (1st Edition, McGraw-Hill Education).
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kspcr111 | In Training Educator

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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

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