Question

What is the slope-intercept form of the equation of the line through the point (-8, 7) and parallel to the line `x + y = 13`?

Answer 1

`y=-x-1`

Explanation:

`"the equation of a line in "color(blue)"slope-intercept form"` is.

`•color(white)(x)y=mx+b`

`"where m is the slope and b the y-intercept"`

`"rearrange "x+y=13" into this form"`

`"subtract "x" from both sides"`

`y=-x+13larrcolor(blue)"in slope-intercept form"`

`"with slope "=-1`

`• " Parallel lines have equal slopes"`

`y=-x+blarrcolor(blue)"is the partial equation"`

`"to find b substitute "(-8,7)" into the partial equation"`

`7=8+brArrb=7-8=-1`

`y=-x-1larrcolor(red)"slope-intercept form of parallel line"`