How do you write the equation in slope intercept form given (4,1):(5,3)?

1 Answer
Jim G.
May 7, 2017

#y=2x-7#

Explanation:

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

#color(red)(bar(ul(|color(white)(2/2)color(black)(y=mx+b)color(white)(2/2)|)))#
#"where m represents the slope and b, the y-intercept"#

#"to calculate the slope 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_2y_2)" are 2 coordinate points"#

#"the 2 points here are " (4,1)" and " (5,3)#

#"let " (x_1,y_1)=(4,1)" and " (x_2,y_2)=(5,3)#

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

#rArry=2x+b#

#"to find b, substitute either of the given points into the"#
#"equation and solve for b"#

#"using " (4,1)#

#1=(2xx4)+b#

#rArrb=1-8=-7#

#rArry=2x-7larrcolor(red)" in slope-intercept form"#

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