Question 1180718

Which equation represents a line which is parallel to the line {{{y=(8/7)x−6}}}?

a line which is parallel to the given line must have {{{same}}} slope and given line has a slope {{{(8/7)}}}

write each in slope intercept form

a. 
{{{8x+7y=35}}}=>{{{7y=-8x+35}}}=>{{{y=-(8/7)x+5}}}=> a slope is {{{not}}} {{{same}}} 
b. 
{{{8x−7y=56}}}=>{{{8x−56=7y}}}=>{{{(8/7)x−8=y}}}=> a slope {{{highlight(IS)}}} {{{same}}} =>a line {{{is}}} parallel to the line {{{y=(8/7)x−6}}}


c.
{{{ 8y−7x=−24}}}=>{{{ 8y=7x−24}}}=>{{{ y=(7/8)x−3}}}=> a slope is {{{not}}} {{{same}}} 

d. 
{{{7x+8y=-8}}}=>{{{8y=-7x-8}}}=>{{{y=-(7/8)x-1}}}=> a slope is {{{not}}} {{{same}}}  (but it is negative reciprocal of the slope of given line, so this line is perpendicular to given line)


so, answer is

b. 
{{{8x−7y=56}}}=>{{{8x−56=7y}}}=>{{{(8/7)x−8=y}}}=> a slope {{{highlight(IS)}}} {{{same}}} =>a line {{{is}}} parallel to the line {{{y=(8/7)x−6}}}


{{{ graph( 600, 600, -10, 10, -10, 10, (8/7)x-6, (8/7)x-8) }}}