See picture, what is the equation of the function? Thanks a lot!

enter image source here

2 Answers
May 10, 2018

#y = -9/2x-2#

Explanation:

Write the equation, #2x-9y-18=0# in slope-intercept form:

#-9y = -2x+18#

#y = 2/9x-2#

Please observe that the slope #m = 2/9# and the y-intercept is #-2#.

The slope, #n#, of a line perpendicular to a line of slope, #m#, is:

#n = -1/m#

Substituting #m = 2/9#:

#n = -1/(2/9)#

#n = -9/2#

Therefore, the equation that is perpendicular and has the same y-intercept is:

#y = -9/2x-2#

May 10, 2018

#y=-9/2x-2#

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 "2x-9y-18=0" into this form"#

#"subtract "2x-18" from both sides"#

#rArr-9y=-2x+18#

#"divide all terms by "-9#

#rArry=2/9x-2larrcolor(blue)"in slope-intercept form"#

#"with slope m "=2/9" and y-intercept "=color(red)(-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#

#rArrm_("perpendicular")=-1/(2/9)=color(magenta)(-9/2)#

#"the required equation has "m=-9/2" and "b=-2#

#rArry=-9/2x-2larrcolor(red)"in slope-intercept form"#