# 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"#