How do you write the point-slope form of the equation given (4,0) and (0,4)?

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Answer 1 · 2018-06-09T15:15:10

#y-0=-1(x-4)#

We have after the formula
#y-y_0=m(x-x_0)#
#m=(y_2-y_1)/(x_2-x_1)=(4-0)/(0-4)=-1#

#y-0=-1(x-4)#

Answer 2 · 2018-06-09T15:16:22

#(y-4) = -1(x-0)#

Slope point formula

First you determine the slope:

#(color(blue)(x_1),color(blue)(y_1)) = (4,0)#

#(color(red)(x_2),color(red)(y_2))=(0,4)#

#color(green)m =(color(red)(y_2)-color(blue)(y_1))/(color(red)(x_2)-color(blue)(x_1))#

#color(green)m =(color(red)(4)-color(blue)(0))/(color(red)(0)-color(blue)(4))=-1#

Now use the Point Slope form of a line:

#(y-color(blue)(y_1)) = color(green)m(x-color(blue)(x_1))#

#(y-color(blue)(4)) = color(green)(-1)(x-color(blue)(0))#

this is the point slope form above, you can simplify to slope intercept form:

#y=-x +4#