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

##### 2 Answers

#### 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"#

#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"#

See details below

#### Explanation:

The general equation of a stright line is

where m is the slope and n is y-intercept

We know also that if m is the slope, then

The reuqested equation is

We dont know what is the n value, but they asking for a line perpendicular passing thru

Transposing terms we found

See graph below (A is the given point)