How do you write the equation in point slope form given (1,3) and (3,-5)?

1 Answer
Jim G.
Mar 28, 2017

#y-3=-4(x-1)#

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 find 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 (1 ,3) and (3 ,-5)

let # (x_1,y_1)=(1,3)" and " (x_2,y_2)=(3,-5)#

#rArrm=(-5-3)/(3-1)=(-8)/2=-4#

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

#"Using " (x_1,y_1)=(1,3)" and " m=-4#

#rArry-3=-4(x-1)larrcolor(red)" in point-slope form"#

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