What is the equation of the line that passes through the points #(4, 7)# and #(-2, 6)#?

2 Answers
Harish Chandra Rajpoot
Jul 27, 2018

#x-6y+38=0#

Explanation:

The equation of straight line passing through the given points #(x_1, y_1)\equiv(4, 7)# & #(x_2, y_2)\equiv(-2, 6)# is given by following formula

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

#y-7=\frac{6-7}{-2-4}(x-4)#

#y-7=\frac{1}{6}(x-4)#

#6y-42=x-4#

#x-6y+38=0#

Jim G.
Jul 27, 2018

#y=1/6x+19/3#

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)=(4,7)" and "(x_2,y_2)=(-2,6)#

#m=(6-7)/(-2-4)=(-1)/(-6)=1/6#

#y=1/6x+clarrcolor(blue)"is the partial equation"#

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

#"using "(-2,6)" then"#

#6=-1/3+crArrc=6+1/3=19/3#

#y=1/6x+19/3larrcolor(red)"equation in slope-intercept form"#

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