What is the equation of the line with slope # m=-4 # that passes through # (4,5) #?

3 Answers
May 11, 2018

#4x+y-21=0#

Explanation:

Using point gradient formula:

#(y-y_1)=m(x-x_1)#
where #(x_1,y_1)# is #(4,5)#

#(y-5)=-4(x-4)#
#y-5=-4x+16#
#4x+y-21=0#

May 11, 2018

#y=-4x+21#

Explanation:

#m=-4# is equivalent to the gradient by #y=mx+c#. The coordinates #(5,4)# indicates that the point occurs when #x=5# and #y=4# and these are free variables that you can plug in for #x# and #y#.

Using the format of #y=mx+c# solve for #c#:

#y=mx+c#
#5=-4(4)+c#
#5=-16+c#
#5+16=c#
#c=21#

Therefore, the equation for the slope is:

#y=-4x+21#

May 11, 2018

Equation of the line is # 4 x + y =21 #

Explanation:

The equation of line passing through #(x_1=4,y_1=5)# having

slope of #m=-4# is #y-y_1=m(x-x_1) ; #

#:. y-5= -4 (x-4) or y-5 = -4 x +16 # or

# 4 x + y =21 ; #

Equation of the line is # 4 x + y =21 ; # [Ans]