What is the equation of the line between #(12,7)# and #(9,14)#?

2 Answers
Harish Chandra Rajpoot
Jul 27, 2018

#7x+3y-105=0#

Explanation:

The equation of the line passing through the points #(x_1, y_1)\equiv(12, 7)# & #(x_2, y_2)\equiv(9, 14)# is given by following formula

#y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)#

#y-7=\frac{14-7}{9-12}(x-12)#

#y-7=-\frac{7}{3}(x-12)#

#3y-21=-7x+84#

#7x+3y-21-84=0#

#7x+3y-105=0#

Jim G.
Jul 27, 2018

#y=-7/3x+35#

Explanation:

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

#•color(white)(x)y=mx+c#

#"where m is the slope and c 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)=(12,7)" and "(x_2,y_2)=(9,14)#

#m=(14-7)/(9-12)=7/(-3)=-7/3#

#y=-7/3x+clarrcolor(blue)"is the partial equation"#

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

#"using "(12,7)" then"#

#7=-28+crArrc=7+28=35#

#y=-7/3x+35larrcolor(blue)"equation in slope-intercept form"#

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