How do you find the equation of the line through #(3, −1)# and #(4, 7)#?

2 Answers
Serena D.
May 6, 2018

#y=8x-25#

Explanation:

Equation of a line in slope-intercept form: #y=mx+b# with #m# as the slope and #b# as the y-intercept

To find the slope using two points #(x_1, y_1)# and #(x_2, y_2)#:
#(y_2-y_1)/(x_2-x_1)#

#(7-(-1))/(4-3)#

#8/1#

#8 rarr# Currently our equation is #y=8x+b#

To find #b#, plug in one of points:

#7=8*4+b#

#7=32+b#

#b=-25#

#y=8x-25#

Jim G.
May 6, 2018

#y=8x-25#

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)=(3,-1)" and "(x_2,y_2)=(4,7)#

#rArrm=(7-(-1))/(4-3)=8/1=8#

#rArry=8x+blarrcolor(blue)"is the partial equation"#

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

#"using "(4,7)" then"#

#7=32+brArrb=7-32=-25#

#rArry=8x-25larrcolor(red)"is the equation of the line"#

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