How do you write the equation in point slope form given (4,5) and (-3,8)?

1 Answer
Jim G.
Jun 3, 2017

#y-5=-3/7(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 points are " (x_1,y_1)=(4,5),(x_2,y_2)=(-3,8)#

#rArrm=(8-5)/(-3-4)=3/(-7)=-3/7#

#(x_1,y_1)" can be either of the 2 given points"#

#"using " (x_1,y_1)=(4,5)" and " m=-3/7#

#rArry-5=-3/7(x-4)larrcolor(red)" in point-slope form"#

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