How do you write the point slope form of the equation given (4,2) and (1,-1)?

1 Answer
Jim G.
Mar 28, 2017

#y-2=(x-4)#

Explanation:

The equation of a line in #color(blue)"point-slope form"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))#
where m represents the slope and # (x_1,y_1)" a point on the line"#

To calculate m, use the #color(blue)"gradient formula"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))#
where # (x_1,y_1),(x_2,y_2)" are 2 coordinate points"#

The 2 points here are (4 ,2) and (1 ,-1)

let # (x_1,y_1)=(4,2)" and " (x_,y_2)=(1,-1)#

#rArrm=(-1-2)/(1-4)=(-3)/(-3)=1#

Use either of the 2 given points for # (x_1,y_1)#

#"Using " (4,2)=(x_1,y_1)" and " m=1#

#y-2=1(x-4)larrcolor(red)" in point slope form"#

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