What is the equation of the line passing through #(13,7)# and #(37,47)#?

1 Answer
Jim G.
May 13, 2018

#5x-3y=44#

Explanation:

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

#•color(white)(x)y=mx+b#

#"where m is the slope and b the y-intercept"#

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

#•color(white)(x)m=(y_2-y_1)/(x_2-x_1)#

#"let "(x_1,y_1)=(13,7)" and "(x_2,y_2)=(37,47)#

#rArrm=(47-7)/(37-13)=40/24=5/3#

#rArry=5/3x+blarrcolor(blue)"is the partial equation"#

#"to find b substitute either of the 2 given points into"#
#"the partial equation"#

#"using "(13,7)" then"#

#7=65/3+brArrb=21/3-65/3=-44/3#

#rArry=5/3x-44/3larrcolor(red)"in slope-intercept form"#

#"multiply all terms by 3 and rearrange"#

#rArr3y=5x-44#

#rArr5x-3y=44larrcolor(red)"in standard form"#

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