"calculate the slope m using the "color(blue)"gradient formula"calculate the slope m using the gradient formula
•color(white)(x)m=(y_2-y_1)/(x_2-x_1)∙xm=y2−y1x2−x1
"let "(x_1,y_1)=(2,3)" and "(x_2,y_2)=(1,-2)let (x1,y1)=(2,3) and (x2,y2)=(1,−2)
m=(-2-3)/(1-2)=(-5)/(-1)=5m=−2−31−2=−5−1=5
"given a line with slope m then the slope of a line"given a line with slope m then the slope of a line
"perpendicular to it is"perpendicular to it is
•color(white)(x)m_(color(red)"perpendicular")=-1/m∙xmperpendicular=−1m
m_("perpendicular")=-1/5mperpendicular=−15
"the equation of a line in "color(blue)"slope-intercept form"the equation of a line in slope-intercept form is.
•color(white)(x)y=mx+c∙xy=mx+c
"where m is the slope and c the y-intercept"where m is the slope and c the y-intercept
y=-1/5x+clarrcolor(blue)"is the partial equation"y=−15x+c←is the partial equation
"to find c substitute "(-5,2)" into the partial equation"to find c substitute (−5,2) into the partial equation
2=1+crArrc=2-1=12=1+c⇒c=2−1=1
y=-1/5x+1larrcolor(red)"equation of perpendicular line"y=−15x+1←equation of perpendicular line
