What is the slope intercept form of the line with a slope of #-2/3 # that passes through # (-5,2) #?

2 Answers
Mar 5, 2018

Answer:

#y=-2/3x-4/3#

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"#

#"here "m=-2/3#

#rArry=-2/3x+blarrcolor(blue)"is the partial equation"#

#"to find b substitute "(-5,2)" into the partial equation"#

#2=10/3+brArrb=6/3-10/3=-4/3#

#rArry=-2/3x-4/3larrcolor(red)"in slope-intercept form"#

Mar 5, 2018

Answer:

#y= -2/3 x -4/3#

Explanation:

#color(blue)(Slope = m)#

#color(blue)(=> -2/3 = (y-y_1)/(x-x_1))#

Here #color(red)(x_1=-5)#

And #color(red)(y_1=2)#

Put them in the above equation

#color(orange)(=> -2/3 = (y-2)/(x-(-5)))#

#color(orange)(=> -2/3 = (y-2)/(x+5))#

Cross-multiply

#color(purple)(=> -2(x+5)=3(y-2))#

#color(purple)(=> -2x -10=3y-6)#

#color(purple)(=> 6-10=2x+3y)#

#color(green)(=> -4-2x=3y)#

#color(green)(=> 3y=-2x-4)#

#color(green)(=> y=-2/3 x -4/3)#