Can you assist me with this? Express the equation in general form or slope-intercept form.
Perpendicular to the line 4x+y=-22, and contains the point (-8,9)
Perpendicular to the line 4x+y=-22, and contains the point (-8,9)
2 Answers
Hence, the equation of the normal is
Explanation:
Given, a straight line
Expressing in standard form
Line is
Comparing we have
Slope of the line
Slope of the normal to the line
The line passes through the point
Intercept given by
The normal in the slope intercept form is
Hence, the equation of the normal is
Explanation:
#"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"#
#"rearrange "4x+y=-22" into this form"#
#"subtract 4x from both sides"#
#cancel(4x)cancel(-4x)+y=-4x-22#
#rArry=-4x-22larrcolor(red)"in slope-intercept form"#
#rArrm=-4#
#"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#
#rArrm_(color(red)"perpendicular")=-1/(-4)=1/4#
#rArry=1/4x+blarrcolor(blue)"is the partial equation"#
#"to find b substitute "(-8,9)" into the partial equation"#
#9=-2+brArrb=9+2=11#
#rArry=1/4x+11larrcolor(red)"in slope-intercept form"#
#"or "x-4y+44=0larrcolor(red)"in general form"#