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
Explanation:
Slope of
Slope of perpendicular line
Equation of line passing through C and perpendicular to
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"#