How do you write the point slope form of the equation given (4,7) and (5,1)?

1 Answer
Jim G.
Apr 5, 2017

#y-1=-6(x-5)#

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 " (4,7)" and " (5,1)#

#"let " (x_1,y_1)=(4,7)" and " (x_2,y_2)=(5,1)#

#rArrm=(1-7)/(5-4)=(-6)/1=-6#

#"For " (x_1,y_1)" use either of the 2 given points"#

#"Using " m=-6" and " (x_1,y_1)=(5,1)#

#rArry-1=-6(x-5)larrcolor(red)" in point-slope form"#

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