Question

How do you write an equation in slope intercept form for the line that satisfies each set of conditions? 1) passes through (-6,15) parallel to the graph of 3x+2y=1 2)passes through (5,-2) perpendicular to the graph of x+2y=8

Answer 1

`y=-3/2x+6" and "y=2x-12`

Explanation:

`(1)`

`• " Parallel lines have equal slopes"`

`"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 "3x+2y=1" into this form"`

`"subtract "3x" from both sides"`

`rArr2y=-3x+1`

`"divide all terms by 2"`

`rArry=-3/2x+1/2larrcolor(blue)"in slope-intercept form"`

`"with slope m "=-3/2`

`"require the equation passing through "(-6,15)`

`rArry=-3/2x+blarrcolor(blue)"is the partial equation"`

`"to find b substitute "(-6,15)" into the partial equation"`

`15=9+brArrb=15-9=6`

`rArry=-3/2x+6larrcolor(red)"is the required equation"`

`(2)`

`"rearrange "x+2y=8" into slope-intercept form"`

`"subtract "x" from both sides and divide by 2"`

`2y=-x+8`

`rArry=-1/2x+4larrcolor(blue)"in slope-intercept form"`

`"with slope m "=-1/2`

`"given a line with slope m then the slope of a line"`
`"perpendicular to it is"`

`•color(white)(x)m_(color(red)"perpendicular")=-1/m`

`rArrm_("perpendicular")=-1/(-1/2)=2`

`"require the equation passing through "(5,-2)`

`rArry=2x+blarrcolor(blue)"is the partial equation"`

`"to find b substitute "(5,-2)" into the partial equation"`

`-2=10+brArrb=-2-10=-12`

`rArry=2x-12larrcolor(red)"is the required equation"`