Equation of the line that is parallel to the line that contains ( -2, 4) and ( 2, 2) and has an x-intercept of 10?

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Answer 1 · 2018-06-28T20:45:35

(-2,4) (2,2) #=>(4-2)/(-2-2)=2/-4=-1/2#

#y=-1/2x+c# can be our original line

If our parallel line has an x intercept of 10 then it passes through (10,0)

#=> 0=-1/2xx10+c#

#0=-5+c#

So #c=5#

Therefore our line is #y=-1/2x+5#

Answer 2 · 2018-06-28T20:46:10

#x+2y-10=0#

The slope #m# of line joining the points #(-2, 4)# & #(2, 2)#
#m=\frac{y_2-y_!}{x_2-x_1}=\frac{2-4}{2-(-2)}=-1/2#

Since the unknown line has x-intercept #10# hence it cut the x-axis at #(10, 0)# i.e. the unknown line passes through the point #(10, 0)#

Now the equation of line having a slope #m=-1/2# & passing through the point #(x_1, y_1)\equiv(10, 0)# is given by point-slope form

#y-y_1=m(x-x_1)#

#y-0=-1/2(x-10)#

#2y=-x+10#

#x+2y-10=0#