What is an equation in slope-intercept form for the line through point P(-5,2) and perpendicular to the line containing the two points (2,3) and (1,-2)?

1 Answer
Jim G.
Aug 13, 2018

#y=-1/5x+1#

Explanation:

#"calculate the slope m using the "color(blue)"gradient formula"#

#•color(white)(x)m=(y_2-y_1)/(x_2-x_1)#

#"let "(x_1,y_1)=(2,3)" and "(x_2,y_2)=(1,-2)#

#m=(-2-3)/(1-2)=(-5)/(-1)=5#

#"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#

#m_("perpendicular")=-1/5#

#"the equation of a line in "color(blue)"slope-intercept form"# is.

#•color(white)(x)y=mx+c#

#"where m is the slope and c the y-intercept"#

#y=-1/5x+clarrcolor(blue)"is the partial equation"#

#"to find c substitute "(-5,2)" into the partial equation"#

#2=1+crArrc=2-1=1#

#y=-1/5x+1larrcolor(red)"equation of perpendicular line"#

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