What is the equation of the line that passes through #(-2,7)# and is perpendicular to the line that passes through the following points: #(1,3),(-5,6) #?

2 Answers
May 25, 2018

Answer:

#color (purple)(2x - y + 11 = 0#

Explanation:

#A(1,3), B(-5,6), C(-2,7)#

Slope of #vec(AB) = m = (y_b - y_a) / (x_b - x_a)#

#m = (6-3) / (-5 - 1) = -(1/2)#

Slope of perpendicular line #= -(1/m) = 2#

Equation of line passing through C and perpendicular to #vec(AB)# is

#y - y_c = -(1/m) * (x - x_c)#

#y - 7 = 2 * (x + 2)#

#y - 7 = 2x + 4#

#color (purple)(2x - y + 11 = 0#

May 25, 2018

Answer:

#y=2x+11#

Explanation:

#"first find the slope m of the line passing through the"#
#"the 2 given points"#

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

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

#"let "(x_1,y_1)=(1,3)" and "(x_2,y_2)=(-5,6)#

#m=(6-3)/(-5-1)=3/(-6)=-1/2#

#"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#

#"hence "m_("perpendicular")=-1/(-1/2)=2#

#"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"#

#"here "m=2#

#y=2x+blarrcolor(blue)"is the partial equation"#

#"to find b substitute "(-2,7)" into the partial equation"#

#7=-4+brArrb=7+4=11#

#y=2x+11larrcolor(red)"is the required equation"#