What is the equation of the line passing through #(1,3), (4,6)#?

2 Answers
Mar 20, 2018

#y=x+2#

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)=(1,3)" and "(x_2,y_2)=(4,6)#

#rArrm=(6-3)/(4-1)=3/3=1#

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

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

#"using "(1,3)" then"#

#3=1+brArrb=3-1=2#

#rArry=x+2larrcolor(red)"is the equation of the line"#

Mar 20, 2018

#y=x+2#

Explanation:

First, we must know what an equation of a line looks like. We write the equation in slope-intercept form:

#y=mx+b#
(The #m# is the slope, and #b# is the y-intercept)

Next, find the slope (#m#) of the line by using the formula #(y_2-y_1)/ (x_2-x_1)#:

#((6)-(3))/((4)-(1))##=##3/3##=##1#

Next, find the y-intercept (#b#) by using the slope-intercept form equation and substituting #1# in for #m# and one of the ordered pairs in for #x# and #y#:

#(3)=(1)(1)+b# #-># #3=1+b# #-># #2=b#
-OR-
#(6)=(1)(4)+b# #-># #6=4+b# #-># #2=b#

Now, we can write the full equation of the line:

#y=x+2#
(We do not need to put a #1# in front of #x# because we know that #1# times any number equals itself)