What is the equation of the line perpendicular to #y=2/7x # that passes through # (-2,9) #?

#"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"#

#y=2/7x" is in this form"#

#"with slope m "=2/7" and "b=0#

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

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

#rArrm_("perpendicular")=-1/(2/7)=-7/2#

#rArry=-7/2x+blarrcolor(blue)"is the partial equation"#

#"to find b substitute "(-2,9)" into the partial equation"#

#9=7+brArrb=9-7=2#

#rArry=-7/2x+2larrcolor(red)"perpendicular equation"#

The general equation of a stright line is #y=mx+n#

where m is the slope and n is y-intercept

We know also that if m is the slope, then #-1/m# is the slope of perpendicular line to the line given. In our case, we have

#m=2/7#, and #n=0# then the slope of perpendicular is #m'=-7/2#

The reuqested equation is #y=-7/2x+n#

We dont know what is the n value, but they asking for a line perpendicular passing thru #(-2,9)#, Then this point acomplish the line equation. That means #9=-7/2·(-2)+n#

Transposing terms we found #n=2#. Finally the equation is

#y=-7/2x+2#
See graph below (A is the given point)