How do you find the slope that is perpendicular to the line #7x+2y=3#?

Question

Ethan Adkins · Accepted Answer

#color(brown)("Slope f the perpendicular line "color(indigo)(m_1 = -(1 / m) = 2/7# #7x + 2y = 3# Standard form of slope intercept equation is #y = mx + c# where m is the slope. #2y = -7x + 3# #y = -(7/2)x + 3/2# Slope of the given line # m = -(7/2)# Slope f the perpendicular line #m_1 = -(1 / m) = -(1 / (-7/2)) = 2/7#

Julia Adams · Answer

#"perpendicular slope "=2/7# #"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 "7x+2y=3" into this form"# #"subtract 7x from both sides"# #cancel(7x)cancel(-7x)+2y=-7x+3# #rArr2y=-7x+3# #"divide all terms by 2"# #rArry=-7/2x+3/2larrcolor(red)"in slope-intercept form"# #"with slope m "=-7/2# #"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/(-7/2)=2/7#

Nathan Axel · Answer

undefined To find the slope perpendicular to the line 7x + 2y = 3, rearrange the equation into slope-intercept form (y = mx + b), where m is the slope. Then, find the negative reciprocal of the slope to get the slope perpendicular to the given line.