# ``passes through the origin, parallel to graph of `x + y = 10` Graph the line that satisfies each set of conditions.

### Textbook Question

Chapter 2, 2.3 - Problem 48 - 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 `(0,0)` , parallel to graph of `x+y=10`

as the slope of the line `x+y=10`  is as follows

`x+y=10`

=> `y = 10 -x`

=>` y = -x +10`

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

so the slope of the line `x+y=10` is `m = -1`

so the line passing through the point `(x,y)=(0,0)` is also `-1 ` as both the lines are parallel

then the line equation passing through (0,0)  is follows

`y= mx+c`

`0 = (-1)(0)+c`

`0= 0 +c`

`c = 0`

so the desired equation of the line is

`y = -x +0`

=>` y = -x or x+y =0`

and it is plotted and in the attachments and the point `(0,0)` is plotted with a blue dot

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